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Quantum Spin Hall Insulator State in HgTe Quantum Wells
Abstract
Recent theory predicted that the quantum spin Hall effect, a fundamentally new quantum state of matter that exists at zero
external magnetic field, may be realized in HgTe/(Hg,Cd)Te quantum wells. We fabricated such sample structures with low density
and high mobility in which we could tune, through an external gate voltage, the carrier conduction from n-type to p-type,
passing through an insulating regime. For thin quantum wells with well width d < 6.3 nanometers, the insulating regime showed the conventional behavior of vanishingly small conductance at low temperature.
However, for thicker quantum wells (d > 6.3 nanometers), the nominally insulating regime showed a plateau of residual conductance close to 2e2/h, where e is the electron charge and h is Planck's constant. The residual conductance was independent of the sample width, indicating that it is caused by edge
states. Furthermore, the residual conductance was destroyed by a small external magnetic field. The quantum phase transition
at the critical thickness, d = 6.3 nanometers, was also independently determined from the magnetic field–induced insulator-to-metal transition. These
observations provide experimental evidence of the quantum spin Hall effect.
... Topological insulators [1,2] are a class of materials defined by a remarkable feature: electronic states at their surfaces are protected by topology and thus cannot be eliminated without closing the energy gap of the insulator. Most research has focused on naturally occurring topological insulating materials [3,4,5,6,7]. But topological states can also be created artificially in the laboratory, by applying design principles derived from the fundamental theory that governs their unusual nature. ...
... The tight-binding Hamiltonian also reproduces the experimentally observed end-state delocalization. This is shown in Fig. 8(b) for the case of N=7 with t1 and t2 adjusted to the experimental hoppings corresponding to (4,3) configuration: the blue bars indicate the squared wave-function coefficients of the end state (n=4) calculated with the onsite energy values derived from the approach described above while the red bars show the result obtained with all onsite energies equal to zero. In the latter case, the end state resides only on the A sites while it becomes delocalized and occurs also the B sites at finite and varying onsite energy. ...
... The conductance spectra in Figs. 4 and 5 revealed that the measured energies En indicate a level spectrum that is not symmetric about its center. A more extensive data set is plotted in Fig. 8 showing the experimental energies (small filled symbols) observed for various individual chains with odd N=3,5,7, and 9 in (4,3) and (5,3) configuration, respectively. ...
Atom manipulation by scanning tunneling microscopy was used to construct quantum dots on the InAs(111)A surface. Each dot comprised six ionized indium adatoms. The positively charged adatoms create a confining potential acting on surface-state electrons, leading to the emergence of a bound state associated with the dot. By lining up the dots into N-dot chains with alternating tunnel coupling between them, quantum-dot molecules were constructed that revealed electronic boundary states as predicted by the Su-Schrieffer-Heeger (SSH) model of one-dimensional topological phases. Dot chains with odd N were constructed such that they host a single end or domain-wall state, allowing one to probe the localization of the boundary state on a given sublattice by scanning tunneling spectroscopy. We found probability density also on the forbidden sublattice together with an asymmetric energy spectrum of the chain-confined states. This deviation from the SSH model arises because the dots are charged and create a variation in onsite potential along the chain - which does not remove the boundary states but shifts their energy away from the midgap position. Our results demonstrate that topological boundary states can be created in quantum-dot arrays engineered with atomic-scale precision.
... Introduction. -Topological Insulators (TIs) are materials that behave as gapped insulators in bulk whereas also hosting metallic (gapless) topological helical states localized at their edges in 2D TIs [1][2][3][4][5][6][7][8][9][10] or surfaces in 3D TIs [11][12][13][14][15][16]. For that reason, attention to topological materials has been mainly focused on edge-and surfacelike phenomena. ...
... For that reason, attention to topological materials has been mainly focused on edge-and surfacelike phenomena. For instance, the corresponding experimental confirmation of TIs are usually performed via edge-or surface-related effects, e.g., the quantized conductivity for 2D TIs [6,[17][18][19], and angle-resolved photoemission spectroscopy for 3D TIs [9,[20][21][22][23]. Despite these successful realizations, there are still open problems, e.g., the quantization of the resistivity is not always observed [6,8,17,[24][25][26][27][28][29]. ...
... For instance, the corresponding experimental confirmation of TIs are usually performed via edge-or surface-related effects, e.g., the quantized conductivity for 2D TIs [6,[17][18][19], and angle-resolved photoemission spectroscopy for 3D TIs [9,[20][21][22][23]. Despite these successful realizations, there are still open problems, e.g., the quantization of the resistivity is not always observed [6,8,17,[24][25][26][27][28][29]. This thus requires the development of alternative methods to probe the presence of topological bands, e.g., via the investigation of bulk properties of the material. ...
We investigate the Shubnikov-de Haas (SdH) magneto-oscillations in the resistivity of two-dimensional topological insulators (TIs). Within the Bernevig-Hughes-Zhang (BHZ) model for TIs in the presence of a quantizing magnetic field, we obtain analytical expressions for the SdH oscillations by combining a semiclassical approach for the resistivity and a trace formula for the density of states. We show that when the non-trivial topology is produced by inverted bands with ''Mexican-hat'' shape, SdH oscillations show an anomalous beating pattern that is {\it solely} due to the non-trivial topology of the system. These beatings are robust against, and distinct from beatings originating from spin-orbit interactions. This provides a direct way to experimentally probe the non-trivial topology of 2D TIs entirely from a bulk measurement. Furthermore, the Fourier transform of the SdH oscillations as a function of the Fermi energy and quantum capacitance models allows for extracting both the topological gap and gap at zero momentum.
... Since the theoretical proposal and experimental observation of 2D [1][2][3][4][5][6] and 3D [7][8][9][10][11][12] topological insulators (TIs), these materials have been the subject of substantial research in condensed matter physics and related areas of science [11,[13][14][15][16][17]. Further investigations soon resulted in the discovery of another important class of topological materials named topological crystalline insulators (TCIs) [18][19][20][21][22]. ...
... In particular, the Na 2 CdSn system investigated here is even more compelling. According to our DFT calculations, its expected bulk energy gap, E g ≈ 234.8 meV, is about one order of magnitude larger than those of 2D TIs based on HgTe/CdTe, InAs/GaSb or InAs 0.85 Bi 0.15 /AlSb quantum wells, for which E g ≲ 30 meV [6,[56][57][58]. Such features showcase this ternary compound as an outstanding candidate for the study of room-temperature topological effects and the development of new nanoelectronic [59][60][61], spintronic [62][63][64], thermoelectric [65][66][67] and optical [68,69] devices. ...
... They can also be potentially obtained via mechanical exfoliation. The DTI Na 2 CdSn represents a promising alternative to conventional small-gap topological insulators in 2D -which usually require the engineering of elaborated quantum wells [5,6,58,99,108]. We are optimistic that our findings will stimulate the experimental verification of the DTI phase in this outstanding candidate for realistic room-temperature applications in nanotechnology, such as nanoelectronic, spintronic, thermoelectric and optical devices. ...
Dual topological insulators (DTIs) are simultaneously protected by time-reversal and crystal symmetries, representing advantageous alternatives to conventional topological insulators. By combining ab initio calculations and the $\mathbf{k}\cdot\mathbf{p}$ approach, here we investigate the electronic band structure of a Na$_2$CdSn tri-atomic layer and derive a low-energy $4\times 4$ effective model consistent with all the symmetries of this material class. We obtain the effective Hamiltonian using the L\"owdin perturbation theory, the folding down technique, and the theory of invariants, and determine its parameters by fitting our analytical dispersion relations to those of ab initio calculations. We then calculate the bulk topological invariants of the system and show that the Na$_2$CdSn tri-atomic layer is a giant-gap (hundreds of meV) quasi-2D DTI characterized by both spin and mirror Chern numbers $-2$. In agreement with the bulk-boundary correspondence theorem, we find that a finite-width strip of Na$_2$CdSn possesses two pairs of counter-propagating helical edge states per interface. We obtain analytical expressions for the edge states energy dispersions and wave functions, which are shown to agree with our numerical calculations. Our work opens a new avenue for further studies of Na$_2$CdSn as a potential DTI candidate with room-temperature applications in areas of technological interest, such as nanoelectronics and spintronics.
... The best fit was found for b 1.1, very close to a linear function. The Fermi velocity from the closest linear fit is plotted in (e) together with that of several Dirac materials and, namely, graphene [23,45], Bi 2 Se 3 [46], HgTe [47], FeSe 0.45 Te 0.55 [48], Cd 3 As 2 [49,50], and Na 3 Bi At half filling an additional state can be extracted from the momentum distribution curve (MDC) fits, overlapped on the image [see markers in Fig. 3(b)], which shows holelike dispersion. At first sight it is reminiscent of the dispersive bands already reported for K 3 C 60 grown on Ag(111) [27,28], yet a side-by-side comparison (Fig. S4 in [30]) reveals that the two cases are distinct with a difference in Fermi velocity of over 70% and a band minimum shallower than 0.2 eV in Ref. [27] vs a bandwidth larger than 0.4 eV in the present study. ...
... 4(c) and 4(d). From a linear fit of the peak positions we find a Fermi velocity v F = (7.1 ± 0.6) × 10 5 ms −1 , comparable to some of the highest values reported for Dirac materials [23,[45][46][47][48][49][50][51] [see Fig. 4(e)]. The position of the crossing point can be determined by extrapolating the dispersion to the unoccupied states and is estimated to be (0.3 ± 0.1) eV above the Fermi level. ...
Molecular crystals are a flexible platform to induce novel electronic phases. Due to the weak forces between molecules, intermolecular distances can be varied over larger ranges than interatomic distances in atomic crystals. On the other hand, the hopping terms are generally small, which results in narrow bands, strong correlations, and heavy electrons. Here, by growing KxC60 fullerides on hexagonal layered Bi2Se3, we show that upon doping the series undergoes a Mott transition from a molecular insulator to a correlated metal and an in-gap state evolves into highly dispersive Dirac-like fermions at half filling, where superconductivity occurs. This picture challenges the commonly accepted description of the low-energy quasiparticles as appearing from a gradual electron doping of the conduction states and suggests an intriguing parallel with the more famous family of the cuprate superconductors. More in general, it indicates that molecular crystals offer a viable route to engineer electron-electron interactions.
... In sharp contrast, the spectra taken at the edge (Fig. 2c, orange curves) reveal a pronounced finite density of states within the insulating gap. The presence of the in-gap state localized at the edge suggests the existence of edge modes [39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55] in the charge density wave phase of Ta 2 Se 8 I. ...
... The edge state decays with a characteristic length of r 0 ≈ 1.25 nm on the crystal side, indicating a strongly confined nature of the edge state. Note that this is nearly 50 times smaller than in HgTe/CdTe quantum wells and 2 times larger than in bismuthene 39,43,55 . The strongly confined nature of the edge state https://doi.org/10.1038/s41567-024-02469-1 is evident in Supplementary Fig. 7, displaying line profiles for the topography and corresponding dI/dV around the step edge. ...
Charge density waves appear in numerous condensed matter platforms ranging from high-temperature superconductors to quantum Hall systems. Despite such ubiquity, there has been a lack of direct experimental study of boundary states that can uniquely stem from the charge order. Here we directly visualize the bulk and boundary phenomenology of the charge density wave in a topological material, Ta2Se8I, using scanning tunnelling microscopy. At a monolayer step edge, we demonstrate the presence of an in-gap boundary mode persisting up to the charge ordering temperature with modulations along the edge that match the charge density wave wavevector along the edge. Furthermore, these results manifesting the presence of an edge state challenge the existing axion insulator interpretation of the charge-ordered phase in this compound.
... The Quantum Spin Hall Effect (QSHE) and topological order represent some of the most exciting advancements in condensed matter physics over the past few decades. The QSHE, a state in which an electrical current flows along the edges of a material without dissipation, was first predicted theoretically in graphene by Kane and Mele in 2005 and subsequently observed experimentally in HgTe quantum wells by König et al. in 2007. This discovery opened new avenues for research into topological insulators, materials that are insulating in the bulk but conductive on their surfaces. ...
... However, the spin-orbit coupling in graphene is weak, making the effect challenging to observe. Subsequently, Bernevig, Hughes, and Zhang predicted that HgTe quantum wells would exhibit the QSHE, a prediction confirmed experimentally by König et al. in 2007. ...
The Quantum Spin Hall Effect (QSHE) and topological order represent groundbreaking advancements in the realm of condensed matter physics, offering new paradigms for understanding electronic properties in materials. The QSHE, characterized by spin-polarized edge states protected by time-reversal symmetry, has been experimentally confirmed in materials such as HgTe quantum wells and monolayer WTe2. Topological order, which extends beyond the traditional symmetry-breaking framework, is defined by global properties and robust edge states immune to local perturbations, playing a crucial role in systems like the fractional quantum Hall effect. This paper provides a comprehensive review of the theoretical background, recent research findings, experimental methods, and potential applications of QSHE and topological order. By exploring key studies, such as the observation of higher-order topological insulators and the discovery of Majorana modes in topological superconductors, we highlight the profound implications for electronics, quantum computing, and material science. The paper also discusses current challenges and future directions in the field, emphasizing the need for materials exhibiting these effects at higher temperatures and scalable methods for producing topological states. The ongoing research promises to revolutionize our understanding of quantum phases and drive technological innovations.
... It supports a bulk gap and dissipationless helical states along the edge. Several candidate materials have been experimentally confirmed to host the QSH phase, including HgTe/CdTe [2] and InAs/GaSb quantum wells (QWs) [3], 1T -WTe 2 monolayer [4], and potentially transition metal dichalcogenide moiré systems [5]. The physics of the QSH states can be well captured with the Bernevig-Hughes-Zhang (BHZ) model [6] or the Kane-Mele model [7] in the singleparticle paradigm. ...
... As is common in condensed matter systems, the resulting phase diagram becomes richer and more interesting as an electronhole bilayer is subject to a magnetic field. Despite some previous experiments under magnetic fields as reported in, e.g., [2,14], no attention was paid to the evidence of Coulomb interaction in those reports. Part of the reason may be that in those deeply inverted InAs/GaSb and HgTe/CgTe QWs studied, the electron-hole (e-h) hybridization dominates and the Coulomb interaction U is nearly negligible compared to the tunneling strength A [15,16]. ...
We report a magneto-induced topological phase transition in inverted InAs/GaSb bilayers from a quantum spin Hall insulator to a normal insulator. We utilize a dual-gated Corbino device in which the degree of band inversion, or equivalently the electron and hole densities, can be continuously tuned. We observe a topological phase transition around the magnetic field where a band crossing occurs, accompanied by a bulk-gap closure characterized by a bulk conductance peak (BCP). In another set of experiments, we study the transition under a tilted magnetic field (tilt angle ). We observe the characteristic magnetoconductance around BCP as a function of , which dramatically depends on the density of the bilayers. In a relatively deep inversion (hence a higher density) regime, where the electron-hole hybridization dominates the excitonic interaction, the BCP grows with . On the contrary, in a shallowly inverted (a lower density) regime, where the excitonic interaction dominates the hybridization, the BCP is suppressed indicating a smooth crossover without a gap closure. This suggests the existence of a low-density, correlated insulator with spontaneous symmetry breaking near the critical point. Our highly controllable electron-hole system offers an ideal platform to study interacting topological states as proposed by recent theories.
Published by the American Physical Society 2024
... In this work, we focus on a particular zincblende heterostructure, the mercury telluridecadmium telluride (HgTe/CdTe) quantum wells (QWs). They have been widely used to study the quantum spin Hall effect and new types of topological phases [17][18][19][20], and traditionally are part of optical and transport experiments involving spin-related observations [21][22][23]. At present, HgTe/CdTe QWs appear together with other topological insulators to construct lowdimensional quantum devices, which can experimentally realize quantum anomalous Hall effects [24][25][26][27][28]. ...
... We shall use a 2D effective Dirac Hamiltonian to describe the surface states in HgTe/CdTe QWs, following the prescription of the references [17][18][19][20], where τ i are the Pauli matrices, s = ±1 is the spin and H −1 (k) = H * +1 (−k) (temporarily reversed). It is convenient to expand the Hamiltonian H s (k) around the center Γ of the first Brillouin zone [18], ...
The time evolution of a wave packet is a tool to detect topological phase transitions in two-dimensional Dirac materials, such as graphene and silicene. Here we extend the analysis to HgTe/CdTe quantum wells and study the evolution of their electron current wave packet, using 2D effective Dirac Hamiltonians and different layer thicknesses. We show that the two different periodicities that appear in this temporal evolution reach a minimum near the critical thickness, where the system goes from normal to inverted regime. Moreover, the maximum of the electron current amplitude changes with the layer thickness, identifying that current maxima reach their higher value at the critical thickness. Thus, we can characterize the topological phase transitions in terms of the periodicity and amplitude of the electron currents.
... The first and paradigmatic example of such Dirac material in 2D is graphene which is a one-atomthick carbon sheet on a honeycomb lattice [1,2]. Since then, the exploration of novel materials has expanded, revealing several examples with intringuing topological features such as topological insulators [3][4][5] and Weyl semimetals [6][7][8]. ...
Semi-Dirac materials in 2D present an anisotropic dispersion relation, linear along one direction and quadratic along the perpendicular one. This study explores the topological properties and the influence of disorder in a 2D semi-Dirac Hamiltonian. Anisotropic edge states appear only in one direction. Their topological protection can be rigorously founded on the Zak phase of the one-dimensional reduction of the semi-Dirac Hamiltonian, parametrically depending on one of the momenta. In general, only a single value of the momentum is topologically protected so these systems can be considered as high order momentum topological insulators. We explore the dependence on the disorder of the edge states and the robustness of the topological protection in these materials. We also explore the consequences of the high order topological protection in momentum space for the transport properties in a two-terminal configuration.
... Quantum spin Hall insulators (QSHIs) are promising nontrivial topological candidates, having an inverted band structure close to the Fermi surface, thus consisting insulating 2D layer and conducting edge states [8][9][10][11]. Due to Kramer's degeneracy, these counterpropagating helical edge states feature pairs of conducting states with the opposite spin-polarization, which are protected by time-reversal symmetry and get gapped out after applying external magnetic field [11][12][13]. Theoretically, for centrosymmetric materials, the electronic band structure follows the relation under space inversion, E(K, ↑) = E(−K, ↑ ), while it is violated at the surface of the material, and bands get split in the momentum space [14] due to Rashba SOI, thus facilitating the spin-momentum locking [15,16]. Spin-dependence of the electronic properties of materials introduced spintronics, an exotic field of research with vast applications in sensors and quantum computing [17]. ...
We report the synthesis, structural characterization, and investigation of electrical transport, magnetic and specific heat properties of bulk semiconducting layered material Ta$_2$Ni$_3$Te$_5$. Ta$_2$Ni$_3$Te$_5$ crystallizes in the centrosymmetric orthorhombic structure with space group Pnma. Temperature-dependent resistivity shows a transition from semiconducting to metallic nature below 7 K. Low-temperature magnetotransport studies show large magnetoresistance with the signature of weak anti-localization (WAL) effect. The magnetoconductivity data has been used to explore the origin of the WAL effect, extract relevant parameters, and study their variation with temperature. The presence of significant electron-phonon interaction is evident from the MR vs. B/R plot (Kohler's plot). Isothermal field-dependent magnetization studies show Berry paramagnetism as the signature for spin-orbit coupling-induced spin-momentum locking. Observation of WAL effect and spin-momentum locking phenomenon demonstrate Ta$_2$Ni$_3$Te$_5$ as a promising low dimensional material for quantum spin Hall insulator-based applications.
... After nearly two decades of the birth of 2D TR TI theory [6][7][8][9], there have been abundant of candidate materials, e.g., HgTe [17,18], InAs/GaSb [19][20][21], WSe 2 [22,23], WTe 2 [24,25], bismuthine [26], germanene [27], AB stacked MoTe 2 /WSe 2 [28], and TaIrTe 4 [29]. However, the transport signature often shows unexpected resistance, i.e., the conductance is less than e 2 h per chan- nel. ...
We study an interacting composite $(1+1/n)$ Abelian helical edge state made of a regular helical liquid carrying charge $e$ and a (fractionalized) helical liquid carrying charge $e/n$. A systematic framework is developed for these composite $(1+1/n)$ Abelian helical edge states with $n=1,2,3$. For $n=2$, the composite edge state consists of a regular helical Luttinger liquid and a fractional topological insulator (the Abelian $Z_4$ topological order) edge state arising from half-filled conjugated Chern bands. The composite edge state with $n=2$ is pertinent to the recent twisted MoTe$_2$ experiment, suggesting a possible fractional topological insulator with conductance $\frac{3}{2}\frac{e^2}{h}$ per edge. Using bosonization, we construct generic phase diagrams in the presence of $weak$ Rashba spin-orbit coupling. In addition to a phase of free bosons, we find a time-reversal symmetry-breaking localized insulator, two perfect positive drag phases, a perfect negative drag phase (for $n=2,3$), a time-reversal symmetric Anderson localization (only for $n=1$), and a disorder-dominated metallic phase analogous to the $\nu=2/3$ disordered fractional quantum Hall edges (only for $n=3$). We further compute the two-terminal edge-state conductance, the primary experimental characterization for the (fractional) topological insulator. Remarkably, the negative drag phase gives rise to an unusual edge-state conductance, $(1-1/n)\frac{e^2}{h}$, not directly associated with the filling factor. We further investigate the effect of an applied in-plane magnetic field. For $n>1$, the applied magnetic field can result in a phase with edge-state conductance $\frac{1}{n}\frac{e^2}{h}$, providing another testable signature. Our work establishes a systematic understanding of the composite $(1+1/n)$ Abelian helical edge, paving the way for future experimental and theoretical studies.
... For application-related devices, spin manipulation plays a dominant role in the study of QDs in external magnetic fields. Studies on topological insulators and Weyl fermions are related to spin effects because they are useful in spin Hall-effect analyses, which may provide a tool for spintronic device fabrication [10,11]. The main focus of such studies is spin-orbit interactions (SOIs). ...
The thermodynamic and magnetic properties of quantum-dot structures subjected to an applied magnetic field were studied, including the longitudinal optical-phonon interaction and the Rashba spin-orbit effect. The Schrödinger equation was solved to determine the energy levels. The partition function was evaluated by summing the accessible energy levels and was then utilized to calculate the thermomagnetic functions. In this paper, we present magnetic properties by considering three interacting polarons. Our results indicated that at = 0 , the susceptibility exhibits diamagnetic behavior for all values of the Rashba spin-orbit parameter. However, the magnetic susceptibility increases with an applied magnetic field, and the system exhibits paramagnetic behavior under moderate magnetic fields. However, in situations with and without the polaron effect, the susceptibility is saturated at 0(∕ 2) under large magnetic fields. In this study, we showed that the Rashba spin-orbit interaction (SOI) strengthens the cutoff magnetic field (the B value at which the magnetic nature of the dot changes from diamagnetic to paramagnetic). Rashba SOIs reduce the mean energy of the system, including polaronic interactions. Under the polaron effect, the heat capacity curve shifts to lower temperatures. A quantitative description of the magnetocaloric effect () as a function of the Wigner and Rashba spin-orbit parameters is presented.
... Our first case study concerns strictly 1D SCs and, in particular, the edge of a two-dimensional quantum spin Hall insulator [47][48][49][50] which is here assumed to feature a conventional pairing gap due to its proximity to a neighboring bulk SC. See Fig. 1 for an illustration. ...
We bring forward a unified framework for the study of the superfluid stiffness and the quantum capacitance of superconducting platforms exhibiting conventional spin-singlet pairing. We focus on systems which in their normal phase contain topological band touching points or crossings, while in their superconducting regime feature a fully gapped energy spectrum. Our unified description relies on viewing these two types of physical quantities as the charge current and density response coefficients obtained for slow spatiotemporal variations of the superconducting phase. Within our adiabatic formalism, the two coefficients are given in terms of Berry curvatures defined in synthetic spaces. Our paper lays the foundation for the systematic description of topological diagonal superfluid responses induced by singularities dictating the synthetic Berry curvatures. We exemplify our approach for concrete one- and two-dimensional models of superconducting topological (semi)metals. We discuss topological phenomena which arise in the superfluid stiffness of bulk systems and the quantum capacitance of Josephson junctions. We show that both coefficients become proportional to a topological invariant which counts the number of topological touchings or crossings of the normal phase band structure. These topological effects can be equivalently viewed as manifestations of chiral anomaly. Our predictions appear experimentally testable in topological semimetals with proximity-induced pairing, such as in graphene-superconductor hybrids at charge neutrality.
Published by the American Physical Society 2024
... In the presence of topological obstructions, symmetric Wannier functions display a polynomial rather than exponential decay around their center. While this nuanced property hasn't been directly measured, current efforts are directed to finding the imposed topological boundary modes [8][9][10][11][12], and bulk electromagnetic responses which are enforced by these obstructions [13][14][15]. ...
Ingap states are commonly observed in semiconductors and are often well characterized by a hydrogenic model within the effective mass approximation. However, when impurities are strong, they significantly perturb all momentum eigenstates, leading to deep-level bound states that reveal the global properties of the unperturbed band structure. In this work, we discover that the topology of band wavefunctions can impose zeros in the impurity-projected Green's function within topological gaps. These zeros can be interpreted as spectral attractors, defining the energy at which ingap states are pinned in the presence of infinitely strong local impurities. Their pinning energy is found by minimizing the level repulsion of band eigenstates onto the ingap state. We refer to these states as ring states, marked by a mixed band character and a node at the impurity site, guaranteeing their orthogonality to the bare impurity eigenstates and a weak energy dependence on the impurity strength. We show that the inability to construct symmetric and exponentially localized Wannier functions ensures topological protection of ring states. Linking ring states together, the edge or surface modes can be recovered for any topologically protected phase. Therefore, ring states can also be viewed as building blocks of boundary modes, offering a framework to understand bulk-boundary correspondence.
... Three-dimensional (3D) TIs feature two-dimensional (2D) Dirac-cone surface states with a momentum-locked spin texture 11 , resulting in the generation of spin currents. In 2D TIs, one-dimensional (1D) topological edge states prevent backscattering and impart a dissipationless characteristic to spin currents, realizing the quantum spin Hall effect 12 . By contrast, further dimensionality reduction to 1D TIs limits conductivity because of the constrained electron motion of approximately zero-dimensional bound states (BSs). ...
Introducing the concept of topology has revolutionized materials classification, leading to the discovery of topological insulators and Dirac–Weyl semimetals1–3. One of the most fundamental theories underpinning topological materials is the Su–Schrieffer–Heeger (SSH) model4,5, which was developed in 1979—decades before the recognition of topological insulators—to describe conducting polymers. Distinct from the vast majority of known topological insulators with two and three dimensions1–3, the SSH model predicts a one-dimensional analogue of topological insulators, which hosts topological bound states at the endpoints of a chain4–8. To establish this unique and pivotal state, it is crucial to identify the low-energy excitations stemming from bound states, but this has remained unknown in solids because of the absence of suitable platforms. Here we report unusual electronic states that support the emergent bound states in elemental tellurium, the single helix of which was recently proposed to realize an extended version of the SSH chain9,10. Using spin- and angle-resolved photoemission spectroscopy with a micro-focused beam, we have shown spin-polarized in-gap states confined to the edges of the (0001) surface. Our density functional theory calculations indicate that these states are attributed to the interacting bound states originating from the one-dimensional array of SSH tellurium chains. Helices in solids offer a promising experimental platform for investigating exotic properties associated with the SSH chain and exploring topological phases through dimensionality control.
... The quantum spin Hall (QSH) effect was first predicted in graphene if the inclusion of spin−orbit coupling (SOC) opens a band gap at the Dirac cone 6 . It was then experimentally realized in HgTe 7,8 and InAs/GaSb 9 quantum wells, but the observation of the QSH effect demands cryogenic temperatures to suppress thermal excitation and bulk conduction, due to the narrow band gaps of 10 meV. To realize the high-temperature QSH effect (up to room temperature), substantial efforts have been made to search for alternative QSH materials with wide band gaps [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] . ...
Two-dimensional topological insulators hosting the quantum spin Hall effect have application potential in dissipationless electronics. To observe the quantum spin Hall effect at elevated temperatures, a wide band gap is indispensable to efficiently suppress bulk conduction. Yet, most candidate materials exhibit narrow or even negative band gaps. Here, via elegant control of van der Waals epitaxy, we have successfully grown monolayer ZrTe5 on a bilayer graphene/SiC substrate. The epitaxial ZrTe5 monolayer crystalizes in two allotrope isomers with different intralayer alignments of ZrTe3 prisms. Our scanning tunneling microscopy/spectroscopy characterization unveils an intrinsic full band gap as large as 254 meV and one-dimensional edge states localized along the periphery of the ZrTe5 monolayer. First-principles calculations further confirm that the large band gap originates from strong spin−orbit coupling, and the edge states are topologically nontrivial. These findings thus provide a highly desirable material platform for the exploration of the high-temperature quantum spin Hall effect.
... The experimental evidence of 2D TIs has been reported in many systems such as HgTe/CdTe [12] and InAs/GaSb [7] having QSHE and Cr-doped (Bi,Sb) 2 Te 3 having QAHE [13] and so on. The implementation of the QSH effect in practical devices is hindered by the need for severe technological constraints, such as its fabrication by carefully controlled molecular-beam epitaxy and ultra low temperatures (because of their small bulk gap of the order of meV). ...
Topological insulator (TIs), a novel quantum state of materials, has a lot of significance in the development of low-power electronic equipments as the conducting edge states display exceptional endurance against back-scattering. The absence of suitable materials with high fabrication feasibility and significant nontrivial bandgap, is now the biggest hurdle in their potential applications in devices. Here, we illustrate using first principles density functional calculations that the quintuplet layers of EuMg2Bi2 and YbMg2Bi2 crystals are potential two-dimensional TIs with a sizeable nontrivial gaps of 72 meV and 147 meV respectively. Dynamical stability of these quintuplet layers of EuMg2Bi2 and YbMg2Bi2 is confirmed by our phonon calculations. The weakly coupled layered structure of parent compounds makes it possible for simple exfoliation from a three-dimensional structure. We observed gapless edge states inside the bulk band gap in both the systems which indicate their TI nature. Further, we observed the anomalous and spin Hall conductivities to be quantized in two dimensional EuMg2Bi2 and YbMg2Bi2 respectively. Our findings predict two viable candidate materials as two dimensional quantum TIs which can be explored by future experimental investigations and possible applications of quantized spin and anomalous Hall conductance in spintronics.
... The number 64 is enclosed in square brackets. The earliest experimental discovery of topological materials, which can achieve a topological state without requiring intricate experimental conditions, occurred ten years ago [60]. Understanding the electrical band structure of topological materials, which have a unique band topology, is currently crucial for comprehending the physical properties of various materials [61]. ...
This review paper examines the crucial role of nanowires in the field of quantum computing, highlighting their importance as versatile platforms for qubits and vital building blocks for creating fault-tolerant and scalable quantum information processing systems. Researchers are studying many categories of nanowires, including semiconductor, superconducting, and topo-logical nanowires, to explore their distinct quantum features that play a role in creating various qubit designs. The paper explores the interdisciplinary character of quantum computing, combining the fields of quantum physics and materials science. This text highlights the significance of quantum gate operations in manipulating qubits for computation, thus creating the toolbox of quantum algorithms. The paper emphasizes the key research areas in quantum technology , such as entanglement engineering, quantum error correction, and a wide range of applications spanning from encryption to climate change modeling. The research highlights the importance of tackling difficulties related to decoding mitigation, error correction, and hardware scalability to fully utilize the transformative potential of quantum computing in scientific, technical , and computational fields.
... Topological phenomena in condensed matter goes back to Ref. [18], where the conductivity of the quantum Hall effect [19] was identified with the first Chern number of the Berry curvature in the reciprocal space. The existence of TIs in two-dimensional HgTe quantum wells was predicted in Ref. [20] and some time later confirmed experimentally [21]. Subsequently, the phenomenon was generalized to three-dimensional systems with theoretical predictions in Refs. ...
Motivated by the recent interest aroused by non-dynamical axionic electrodynamics in the context of topological insulators and Weyl semimetals, we discuss a simple model of the magnetoelectric effect in terms of a $$\theta$$ θ -scalar field that interacts through a delta-like potential located at a planar interface. Thus, in the bulk regions the field is constructed by standard free waves with the absence of evanescent components. These waves have to be combined into linear superposition to account for the boundary conditions at the interface in order to yield the corresponding normal modes. Our aim is twofold: first we quantize the $$\theta$$ θ -scalar field using the normal modes in the canonical approach and then we look for applications emphasizing the effect of momentum non-conservation due to the presence of the interface. To this end, we calculate the decay of a standard scalar particle into two $$\theta$$ θ -scalar particles showing the opening of new decay channels. As a second application, we deal with the two-body scattering of standard charged scalar particles mediated by a $$\theta$$ θ -scalar particle, focusing on the momentum non-conserving contribution of the scattering amplitude $${{\mathcal {M}}}^{NC}$$ M NC . We define a generalization of the usual cross section in order to quantify the emergence of these events. We also study the allowed kinematical region for momentum non-conservation as well as the position of the poles of the amplitude $${{\mathcal {M}}}^{NC}$$ M NC . Finally, the ratio of the magnitudes between $${{\mathcal {M}}}^{NC}$$ M NC and the momentum conserving amplitude is discussed in the appropriate region of momentum space.
... Gate defined lateral junctions in the ambipolar two-dimensional topological insulator mercury telluride [10,11] have been used to probe the interaction of quantum Hall (chiral) and quantum spin Hall (helical) edge channels [12,13]. Gusev et al [12] combine a n-doped quantum well with a top gated strip, which forms a nxn junction (x = n ′ , i, p). ...
We present overlapping top gate electrodes for the formation of gate defined lateral junctions in semiconducting layers as an alternative to the back gate/top gate combination and to the split gate configuration. The optical lithography microfabrication of the overlapping top gates is based on multiple layers of low-temperature atomic layer deposited hafnium oxide, which acts as a gate dielectric and as a robust insulating layer between two overlapping gate electrodes exhibiting a large dielectric breakdown field of >1×109V m−1 . The advantage of overlapping gates over the split gate approach is confirmed in model calculations of the electrostatics of the gate stack. The overlapping gate process is applied to Hall bar devices of mercury telluride in order to study the interaction of different quantum Hall states in the nn′, np, pn and pp′ regime.
... Two-dimensional topological insulators (2D TI) are of scientific interest due to the quantum spin Hall effect that occurs in such materials and its potential applications in spintronic devices and topological quantum computation [1][2][3][4][5][6]. To observe the topological edge states in a transport experiment, it is necessary to position the Fermi energy within the * Author to whom any correspondence should be addressed. ...
Two-dimensional topological insulators have attracted much interest due to their potential applications in spintronics and quantum computing. To access the exotic physical phenomena, a gate electric field is required to tune the Fermi level into the bulk band gap. Hexagonal boron nitride (h-BN) is a promising alternative gate dielectric due to its unique advantages such as flat and charge-free surface. Here we present a h-BN/graphite van der Waals heterostructure as a top gate on HgTe heterostructure-based Hall bar devices. We compare our results to devices with h-BN/Ti/Au and HfO2/Ti/Au gates. Devices with a h-BN/graphite gate show no charge carrier density shift compared to as-grown structures, in contrast to a significant n-type carrier density increase for HfO2/Ti/Au. We attribute this observation mainly to the comparable work function of HgTe and graphite. In addition, devices with h-BN gate dielectric show slightly higher electron mobility compared to HfO2-based devices. Our results demonstrate the compatibility between layered materials transfer and wet-etched structures and provide a strategy to solve the issue of significant shifts of the carrier density in gated HgTe heterostructures.
... Later, Haldane put forward the quantum Hall effect without Landau levels in graphene by adding periodic magnetic flux [45]. Kane-Mele predicted the quantum spin Hall insulator [two-dimensional (2D) TIs] in 2005, which is the spin version of quantum Hall effect [46,47], and this interesting phase was confirmed in HgTe quantum well later [48][49][50]. Subsequently, the 2D TIs were generalized to three-dimensional (3D) cases [51][52][53][54], which are divided into strong and weak TIs, hosting metallic surface states but with an odd and even number of Dirac cones, respectively. ...
Recently, topolectrical circuits (TECs) boom in studying the topological states of matter. The resemblance between circuit Laplacians and tight-binding models in condensed matter physics allows for the exploration of exotic topological phases on the circuit platform. In this review, we begin by presenting the basic equations for the circuit elements and units, along with the fundamentals and experimental methods for TECs. Subsequently, we retrospect the main literature in this field, encompassing the circuit realization of (higher-order) topological insulators and semimetals. Due to the abundant electrical elements and flexible connections, many unconventional topological states like the non-Hermitian, nonlinear, non-Abelian, non-periodic, non-Euclidean, and higher-dimensional topological states that are challenging to observe in conventional condensed matter physics, have been observed in circuits and summarized in this review. Furthermore, we show the capability of electrical circuits for exploring the physical phenomena in other systems, such as photonic and magnetic ones. Importantly, we highlight TEC systems are convenient for manufacture and miniaturization because of their compatibility with the traditional integrated circuits. Finally, we prospect the future directions in this exciting field, and connect the emerging TECs with the development of topology physics, (meta)material designs, and device applications.
... A class of semiconductor heterostructures with large Rashba SOC and high electron mobility is identified n the SM Sec.II.B for possible material realizations of moiré Rashba systems. The BHZ model can be realized by HgTe/CdTe QWs [36,62], InAs/GaSb QWs [38,63], and monolayer 1T ′ -WTe 2 [64]. The superlattice potential could be created by moiré 2D insulating materials, such as boron nitride or transition metal dichalcogenides [65][66][67][68][69][70], or by the patterned hole array in dielectric substrate materials to form a superlattice potential [71,72]. ...
The emergence of topologically non-trivial flat bands in moir\'e materials provides an opportunity to explore the interplay between topological physics and correlation effects, leading to the recent experimental realization of interacting topological phases, e.g. fractional Chern insulators. In this work, we propose a mechanism of band inversion induced by band-folding from the moir\'e superlattice potential for engineering topological minibands in moir\'e materials. We illustrate this mechanism via two classes of model Hamiltonians, namely the Rashba model and the Bernevig-Hughes-Zhang (BHZ) model, under the moir\'e superlattice potentials. Moir\'e minibands with non-trivial band topology, including Z2 number, mirror Chern number and fragile topology, have been found and the topological phase diagram is constructed for these moir\'e models. A general theory based on band representations in the mori\'e Brillouin zone is also developed for a generalization of this mechanism to other space groups. Possible experimental realizations of our model Hamiltonian are discussed.
... The discovery of topological insulators and superconductors has enlarged the notion of topological phases that owe their properties to symmetries [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. These topological phases are dubbed Symmetry-Protected Topological phases (SPTs), and their key features are bulk energy gaps and edge modes that are robust to symmetrypreserving perturbations. ...
We adapt the fluid description of Fractional Quantum Hall (FQH) states, as seen in (arXiv:2203.06516), to model a system of interacting two-component bosons. This system represents the simplest physical realization of an interacting bosonic Symmetry-Protected Topological (SPT) phase, also known as the integer quantum Hall effect (IQHE) of bosons. In particular, we demonstrate how the fluid dynamical boundary conditions of no-penetration and no-stress at a hard wall naturally give rise to the two counter-propagating boundary modes expected in these SPT phases. Moreover, we identify energy-conserving hydro boundary conditions that can either create a gap in these edge modes or completely isolate the edge states from the bulk, as described in (Physical Review X 14, 011057 (2024)), where they are termed fragile surface states. These fragile surface states are typically absent in K-matrix edge theories and require bulk dynamics to manifest. By leveraging insights from hydrodynamical boundary dynamics, we can further elucidate the intricate surface properties of SPTs beyond the usual topological quantum field theory based approaches.
Magnetization (M) of HgTe, a non-superconducting and topological insulator at ambient pressure, has been calculated by using the mean field theory (MFT) and three different levels of perturbation in the exchange interaction. The spin distribution of Te solely controls the total magnetic contribution which exhibits no oscillating behavior as a function of 1/H even at a temperature of 200.0 mK and magnetic field of 25 T. Nonlinearity in M (H) arises for a suitable perturbation and lower T. The asymmetric nature of M (H) reveals that magnetic fluctuations are unequal to the polarity of the field. Uneven pinning of spins in HgTe in H may suppress the quantum fluctuations. Variations of the spin susceptibility with T exhibit peaks associated with magnetic phase transitions. However, peaks are not related to the quantum oscillations even in the presence of the perturbation. Spin distribution in a nanosized system of HgTe does now exhibit quantum oscillations down to 200 mK and 25 T within the framework of the MFT.
We investigate the effects of electronic correlations on the Bernevig-Hughes-Zhang model using the real-space density matrix renormalization group (DMRG) algorithm. We introduce a method to probe topological phase transitions in systems with strong correlations using DMRG, substantiated by an unsupervised machine learning methodology that analyzes the orbital structure of the real-space edges. Including the full multi-orbital Hubbard interaction term, we construct a phase diagram as a function of a gap parameter (m) and the Hubbard interaction strength (U) via exact DMRG simulations on N×4 cylinders. Our analysis confirms that the topological phase persists in the presence of interactions, consistent with previous studies, but it also reveals an intriguing phase transition from a paramagnetic to a stripey antiferromagnetic topological insulator. The combination of the magnetic structure factor, strength of magnetic moments, and the orbitally resolved density, provides real-space information on both topology and magnetism in a strongly correlated system.
The simultaneous breaking of time-reversal and inversion symmetry can lead to peculiar effects in Josephson junctions, such as the anomalous Josephson effect or supercurrent rectification, which is a dissipationless analog of the diode effect. Due to their impact in new quantum technologies, it is important to find robust platforms and external means to manipulate the above-mentioned effects in a controlled way. Here, we theoretically consider a Josephson junction based on a quantum spin Hall system as the normal channel, subjected to a magnetic field in the direction defined by spin-momentum locking, and in the presence of a local tip in close proximity to one of the metallic edges in the normal region. We consider different local perturbations, model normal and magnetic tips, and study how they affect the Josephson response of the device. In particular, we argue that magnetic tips are a useful tool that allows for tunability of both ϕ0 response and supercurrent rectification.
Understanding electron quantum transport and their coupling interactions in 2D matrix is crucial for manipulating and designing more efficient energy conversion devices, especially in the context of spin transport. Here, we systematically calculate the electronic dispersion properties which the synergistic interaction of the three‐band accounted for the topological transport of edge correlated electrons. The helical state protected by the topology appears at the boundary, accompanied by the upward movement (∼0.2 eV) of the helical point caused by the excitation and the loop channel, which the weak braiding effect reveal local strongly correlated interactions between the boundary electrons. In addition, we also introduce spin Hall conductance and Z2 topological invariants to describe the election dispersion of the topological transport. This provides more possibilities for the realization of topological quantum computing application.
The one-dimensional Su-Schrieffer-Heeger (SSH) model is central to band topology in condensed matter physics, which allows us to understand and design distinct topological states. In this work we find another mechanism to analogize the SSH model in a spinful system, realizing an obstructed atomic insulator by introducing intrinsic spin-orbit coupling and in-plane Zeeman field. In our model the midgap states originate from a quantized hidden polarization with invariant index Z2 (0; 01) due to the local inversion symmetry breaking. When the global inversion symmetry is broken, a charge pumping is designed by tuning the polarization. Moreover, by introducing the p+ip superconductor pairing potential, a topological phase dubbed obstructed superconductor (OSC) is identified. This new state is characterized by invariant index Z2 (0; 01) and nonchiral midgap states. More interestingly, these nonchiral edge states result in a chiral-like nonlocal conductance, which is different from the traditional chiral topological superconductor. Our findings not only find another strategy to achieve a spinful SSH model but also predict the existence of OSC, providing a promising avenue for further exploration of its transport properties.
As a new quantum state, topological insulators have become the focus of condensed matter and material science. The open system research of topological insulators has aroused the interest of many researchers. In this paper, we study the response of topological insulators to a single-mode quantized field with momentum. We solve the ground state of the system after the addition of a single-mode light field with adjustable photon momentum. To be specific, the analytical solution of Hall conductance has an additional correction compared with the closed system, and the Hall conductance can no longer be expressed by the weighted sum of the Chern numbers. Furthermore, the topological properties are analyzed and discussed through the results of an instance with their illustration. The system still has a topological phase transition and the critical point of the topological phase is robust to the single-mode quantized field.
SrIrO$_3$ is a metallic complex oxide with unusual electronic and magnetic properties believed to originate from electron correlations due to its proximity to Mott metal-insulator transition. However, the nature of its electronic state and the mechanism of metallic conduction remain poorly understood. We demonstrate that shot noise produced by nanoscale SrIrO$_3$ junctions is strongly suppressed, inconsistent with diffusive quasiparticle transport. Analysis of thermal effects and scaling with the junction length reveals that conduction is mediated by collective hopping of electrons almost localized by correlations. Our results provide insight into the non-Fermi liquid state close to Mott transition, and advance shot noise measurements as a powerful technique for the studies of quantum materials.
Studies of the formation of Landau levels based on the Schrödinger equation for electrons constrained to curved surfaces have a long history. These include as prime examples surfaces with constant negative curvature, like the pseudosphere [A. Comtet, Ann. Phys. 173, 85 (1987)]. Now, topological insulators, hosting Dirac-type surface states, provide a unique platform to experimentally examine such quantum Hall physics in curved space. Hence, extending previous work we consider solutions of the Dirac equation for the pseudosphere for both the case of an overall perpendicular magnetic field and a homogeneous coaxial, thereby locally varying, magnetic field. For both magnetic-field configurations, we provide analytical solutions for spectra and eigenstates. For the experimentally relevant case of a coaxial magnetic field we find that the Landau levels split and one class shows a peculiar scaling ∝B1/4, thereby characteristically differing from the usual linear B and B1/2 dependence of the planar Schrödinger and Dirac case, respectively. We compare our analytical findings to numerical results that we also extend to the case of the Minding surface.
We consider two-dimensional (2d) quantum many-body systems with long-range orders, where the only gapless excitations in the spectrum are Goldstone modes of spontaneously broken continuous symmetries. To understand the interplay between classical long-range order of local order parameters and quantum order of long-range entanglement in the ground states, we study the topological point defects and textures of order parameters in such systems. We show that the universal properties of point defects and textures are determined by the remnant symmetry enriched topological order in the symmetry-breaking ground states with a nonfluctuating order parameter, and provide a classification for their properties based on the inflation-restriction exact sequence. We highlight a few phenomena revealed by our theory framework. First, in the absence of intrinsic topological orders, we show a connection between the symmetry properties of point defects and textures to deconfined quantum criticality. Second, when the symmetry-breaking ground state has intrinsic topological orders, we show that the point defects can permute different anyons when braided around. They can also obey projective fusion rules in the sense that multiple vortices can fuse into an Abelian anyon, a phenomenon for which we coin “defect fractionalization.” Finally, we provide a formula to compute the fractional statistics and fractional quantum numbers carried by textures (skyrmions) in Abelian topological orders.
Non-Abelian topological phases (NATPs) exhibit enigmatic intrinsic physics distinct from well-established Abelian topological phases, while lacking straightforward configuration and manipulation, especially for classical waves. In this Letter, we exploit novel braiding-type couplings among a pair of triple-component acoustic dipoles, which act as functional elements with effective imaginary couplings. Sequencing them in one dimension allows us to generate acoustic NATPs in a compact yet time-reversal invariant Hermitian system. We further provide the whole phase diagram that encompasses all i, j, and k non-Abelian phases, and directly demonstrate their unique quotient relations via different end point states. Our NATPs based on real-space braiding may inspire the exploration of acoustic devices with non-commutative characters.
Meta-structures, including metamaterials and metasurfaces, possess remarkable physical properties beyond those observed in natural materials and thus have exhibited unique wave manipulation abilities ranging from quantum to classical transports. The past decades have witnessed the explosive development and numerous implications of meta-structures in elastic-wave control under the Hermitian condition. However, more notably, a lot of recent research has been made to show that non-Hermitian meta-structures offer novel means for wave manipulation. Non-Hermiticity has enhanced both the accuracy and efficiency of wave steering capabilities. To this end, starting from electromagnetics and acoustics, we mainly review the up-to-date progress of non-Hermitian elastic meta-structures with a focus on their extraordinary elastic-wave control. A variety of promising scenarios realized by non-Hermitian elastic metamaterials and metasurfaces, such as the parity-time-symmetric system and the skin effect, are summarized. Furthermore, the perspectives and challenges of non-Hermitian elastic meta-structures for future key opportunities are outlined.
The defects have a remarkable influence on the electronic structures and the electric transport behaviors of the matter, providing the additional means to engineering their physical properties. In this work, a comprehensive study on the effect of Br-vacancies on the electronic structures and transport behaviors in the high-order topological insulator Bi4Br4 is performed by the combined techniques of the scanning tunneling microscopy (STM), angle-resolved photoemission spectroscopy (ARPES), and physical properties measurement system along with the first-principle calculations. The STM results show the defects on the cleaved surface of a single crystal and reveal that the defects are correlated to the Br-vacancies with the support of the simulated STM images. The role of the Br-vacancies in the modulation of the band structures has been identified by ARPES spectra and the calculated energy-momentum dispersion. The relationship between the Br-vacancies and the semiconducting-like transport behaviors at low temperature has been established, implying a Mott variable ranging hopping conduction in Bi4Br4. The work not only resolves the unclear transport behaviors in this matter, but also paves a way to modulate the electric conduction path by the defects engineering.
Motivated by the highly anisotropic nature of bulk hafnium pentatelluride (HfTe5), the structural, vibrational, electronic, optical, and elastic properties of single-layer two-dimensional (2D) HfTe5 were investigated by performing density functional theory (DFT)-based first-principles calculations. Total energy and geometry optimizations reveal that the 2D single-layer form of HfTe5 exhibits in-plane anisotropy. The phonon band structure shows dynamic stability of the free-standing layer and the predicted Raman spectrum displays seven characteristic Raman-active phonon peaks. In addition to its dynamic stability, HfTe5 is shown to exhibit thermal stability at room temperature, as confirmed by quantum molecular dynamics simulations. Moreover, the obtained elastic stiffness tensor elements indicate the mechanical stability of HfTe5 with its orientation-dependent soft nature. The electronic band structure calculations show the indirect-gap semiconducting behavior of HfTe5 with a narrow electronic band gap energy. The optical properties of HfTe5, in terms of its imaginary dielectric function, absorption coefficient, reflectance, and transmittance, are shown to exhibit strong in-plane anisotropy. Furthermore, structural analysis of several point defects and their oxidized structures was performed by means of simulated STM images. Among the considered vacancy defects, namely , , VTeout, VTein, , and VHf, the formation of VTeout is revealed to be the most favorable defect. While and VHf defects lead to local magnetism, only the oxygen-substituted VHf structure possesses magnetism among the oxidized defects. Moreover, it is found that all the bare and oxidized vacant sites can be distinguished from each other through the STM images. Overall, our study indicates not only the fundamental anisotropic features of single-layer HfTe5, but also shows the signatures of feasible point defects and their oxidized structures, which may be useful for future experiments on 2D HfTe5.
Topological insulators, featuring bulk-boundary correspondence, have been realized on a large number of noncrystalline materials, among which amorphous network, quasicrystals, and fractal lattices are the most prominent ones. By contrast, topological superconductors beyond the realm of quantum crystals are yet to be harnessed, as their nucleation takes place around a well-defined Fermi surface with a Fermi momentum, the existence of which rests on the underlying translational symmetry. Here we identify a family of noncrystalline Dirac materials, devoid of time-reversal (T) and translational symmetries, on which a suitable local or on-site pairing yields topological superconductors. We showcase this outcome on all the abovementioned noncrystalline platforms embedded in a two-dimensional flat space. The resulting noncrystalline topological superconductors possess quantized topological invariants (Bott index and local Chern marker) and harbor robust one-dimensional Majorana edge modes, analogs of T-odd p+ip pairing in noncrystalline materials.
The demonstration of a topological band inversion constitutes the most elementary proof of a quantum spin Hall insulator (QSHI). On a fundamental level, such an inverted band gap is intrinsically related to the bulk Berry curvature, a gauge-invariant fingerprint of the wave function’s quantum geometric properties in Hilbert space. Intimately tied to orbital angular momentum (OAM), the Berry curvature can be, in principle, extracted from circular dichroism in angle-resolved photoemission spectroscopy (CD-ARPES), were it not for interfering final state photoelectron emission channels that obscure the initial state OAM signature. Here, we outline a full-experimental strategy to avoid such interference artifacts and isolate the clean OAM from the CD-ARPES response. Bench-marking this strategy for the recently discovered atomic monolayer system indenene, we demonstrate its distinct QSHI character and establish CD-ARPES as a scalable bulk probe to experimentally classify the topology of two-dimensional quantum materials with time reversal symmetry.
A new effect in semiconductor spintronics that leads to dissipationless spin currents in paramagnetic spin-orbit coupled systems was described. It was shown that in a high-mobility two-dimensional electron system with substantial Rashba spin-orbit coupling, a spin current that flows perpendicular to the charge current was intrinsic. The intrinsic spin-Hall conductivity has a universal value for zero quasiparticle spectral broadening, where both spin-orbit split bands were occupied. The dynamics of an electron spin in the presence of time-dependent Zeeman coupling was described by using Bloch equation.
The band structure of semimagnetic Hg1−yMnyTe∕Hg1−xCdxTe type-III quantum wells (QW’s) has been calculated using an eight-band k∙p model in an envelope function approach. Details of the band structure calculations are given for the Mn-free case (y=0). A mean-field approach is used to take the influence of the sp-d exchange interaction on the band structure of QW’s with low Mn concentrations into account. The calculated Landau level fan diagram and the density of states of a Hg0.98Mn0.02Te∕Hg0.3Cd0.7Te QW are in good agreement with recent experimental transport observations. The model can be used to interpret the mutual influence of the two-dimensional confinement and the sp-d exchange interaction on the transport properties of Hg1−yMnyTe∕Hg1−xCdxTe QW’s.
The transport properties of micrometer scale structures fabricated from high-mobility HgTe quantum wells have been investigated. A special photoresist and Ti masks were used, which allow for the fabrication of devices with characteristic dimensions down to 0.45 μm. Evidence that the transport properties are dominated by ballistic effects in these structures is presented. Monte Carlo simulations of semiclassical electron trajectories show good agreement with the experiment. © 2003 American Institute of Physics.
HgTe/Hg0.3Cd0.7Te(0 0 1) quantum well structures fabricated with a Si–O–N insulator layer and an Au top gate electrode exhibit hysteresis effects in their gate-voltage dependent carrier density and thus a nonlinear variation of the Rashba spin–orbit splitting energy (ΔR). Charging and discharging of states at the semiconductor insulator interface has been found to be responsible for this effect. The quantitative agreement with a simple capacitor model has been used to identify the maximum hysteresis-free gate-voltage range. A nearly linear variation of ΔR with applied gate voltage has been observed in this range.
Electrically induced electron-spin polarization near the edges of a semiconductor channel was detected and imaged with the
use of Kerr rotation microscopy. The polarization is out-of-plane and has opposite sign for the two edges, consistent with
the predictions of the spin Hall effect. Measurements of unstrained gallium arsenide and strained indium gallium arsenide
samples reveal that strain modifies spin accumulation at zero magnetic field. A weak dependence on crystal orientation for
the strained samples suggests that the mechanism is the extrinsic spin Hall effect.
When electrons are confined in two-dimensional materials, quantum-mechanically enhanced transport phenomena such as the quantum Hall effect can be observed. Graphene, consisting of an isolated single atomic layer of graphite, is an ideal realization of such a two-dimensional system. However, its behaviour is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron-hole degeneracy and vanishing carrier mass near the point of charge neutrality. Indeed, a distinctive half-integer quantum Hall effect has been predicted theoretically, as has the existence of a non-zero Berry's phase (a geometric quantum phase) of the electron wavefunction--a consequence of the exceptional topology of the graphene band structure. Recent advances in micromechanical extraction and fabrication techniques for graphite structures now permit such exotic two-dimensional electron systems to be probed experimentally. Here we report an experimental investigation of magneto-transport in a high-mobility single layer of graphene. Adjusting the chemical potential with the use of the electric field effect, we observe an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these experiments is confirmed by magneto-oscillations. In addition to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.
Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrödinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.
Ring structures fabricated from HgTe/HgCdTe quantum wells have been used to study Aharonov-Bohm type conductance oscillations as a function of Rashba spin-orbit splitting strength. We observe nonmonotonic phase changes indicating that an additional phase factor modifies the electron wave function. We associate these observations with the Aharonov-Casher effect. This is confirmed by comparison with numerical calculations of the magnetoconductance for a multichannel ring structure within the Landauer-Büttiker formalism.
We report the experimental observation of the spin-Hall effect in a two-dimensional (2D) hole system with Rashba spin-orbit coupling. The 2D hole layer is a part of a p-n junction light-emitting diode with a specially designed co-planar geometry which allows an angle-resolved polarization detection at opposite edges of the 2D hole system. In equilibrium the angular momenta of the Rashba split heavy hole states lie in the plane of the 2D layer. When an electric field is applied across the hole channel a non zero out-of-plane component of the angular momentum is detected whose sign depends on the sign of the electric field and is opposite for the two edges. Microscopic quantum transport calculations show only a weak effect of disorder suggesting that the clean limit spin-Hall conductance description (intrinsic spin-Hall effect) might apply to our system. Comment: 4 pages, 3 figures, paper based on work presented at the Gordon Research Conference on Magnetic Nano-structures (August 2004) and Oxford Kobe Seminar on Spintronics (September 2004); accepted for publication in Physical Review Letters December 2004
We show that a PbTe-type narrow-gap semiconductor with an antiphase boundary (or domain wall) has currents of abnormal parity and induced fractional charges. A model is introduced which reduces the problem to the physics of a Dirac equation with a soliton in background electric and magnetic fields. We show that this system is a physical realization of the parity anomaly.
In the inverted-band regime of HgTe/CdTe quantum wells, the lowest Landau level of the lowest conduction subband and the highest Landau level of the topmost valence subband are predicted to cross at a critical magnetic field Bc. We study this crossing experimentally with far-infrared Fourier-transform spectroscopy in a gated HgTe/CdTe quantum well with tunable electron density. The crossing point is identified by a characteristic exchange of oscillator strength between the two transitions involved, one being a cyclotron resonance, the other an intersubband resonance. The experimental resonance positions, the oscillator strengths as well as the value of Bc, are in good agreement with theoretical results of a 6×6 k.p model evaluated for the [211] growth direction.
The influence of interfaces in the structure of HgTe based quantum wells (QW's), their structure as well as the necessary technological processes on their transport properties have been investigated and either reduced or optimized. The mobility (μ) of the 2-dimensional electron gas (2DEG) has been shown to increase when the separation of the 2DEG from the ionized donors is increased, and when the separation of the QW structure from both the insulator on top and the CdTe buffer interface is increased. Furthermore, replacing wet chemical etching in the Hall bar photolithography procedure with a dry plasma etch process resulted in a 2.5 fold increase in the μ. Values for μ up to 0.7 × 106 cm2/(Vs) at 4.2 K have been reproducibly achieved. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
We show that a PbTe-type narrow-gap semiconductor with an antiphase boundary (or domain wall) has currents of abnormal parity and induced fractional charges. A model is introduced which reduces the problem to the physics of a Dirac equation with a soliton in background electric and magnetic fields. We show that this system is a physical realization of the parity anomaly.
Although microscopic laws of physics are invariant under the reversal of the arrow of time, the transport of energy and information in most devices is an irreversible process. It is this irreversibility that leads to intrinsic dissipations in electronic devices and limits the possibility of quantum computation. We theoretically predict that the electric field can induce a substantial amount of dissipationless quantum spin current at room temperature, in hole-doped semiconductors such as Si, Ge, and GaAs. On the basis of a generalization of the quantum Hall effect, the predicted effect leads to efficient spin injection without the need for metallic ferromagnets. Principles found here could enable quantum spintronic devices with integrated information processing and storage units, operating with low power consumption and performing reversible quantum computation.
Recent theories predict dissipationless spin current induced by an electric field in doped semiconductors. Nevertheless, the charge current is still dissipative in these systems. In this work, we theoretically predict the dissipationless spin-Hall effect, without any accompanying charge current, in some classes of band insulators, including zero-gap semiconductors such as HgTe and narrow-gap semiconductors such as PbTe. This effect is similar to the quantum-Hall effect in that all the states below the gap contribute and there occurs no dissipation. However, the spin-Hall conductance is not quantized even in two dimensions. This is the first example of a nontrivial topological structure in a band insulator without any magnetic field.
The quantum spin Hall (QSH) phase is a time reversal invariant electronic state with a bulk electronic band gap that supports the transport of charge and spin in gapless edge states. We show that this phase is associated with a novel Z2 topological invariant, which distinguishes it from an ordinary insulator. The Z2 classification, which is defined for time reversal invariant Hamiltonians, is analogous to the Chern number classification of the quantum Hall effect. We establish the Z2 order of the QSH phase in the two band model of graphene and propose a generalization of the formalism applicable to multiband and interacting systems.
The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. The existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external magnetic field. In this work, we predict a quantized spin Hall effect in the absence of any magnetic field, where the intrinsic spin Hall conductance is quantized in units of 2(e/4pi). The degenerate quantum Landau levels are created by the spin-orbit coupling in conventional semiconductors in the presence of a strain gradient. This new state of matter has many profound correlated properties described by a topological field theory.
The edge states of the recently proposed quantum spin Hall systems constitute a new symmetry class of one-dimensional liquids dubbed the "helical liquid," where the spin orientation is determined by the direction of electron motion. We prove a no-go theorem which states that a helical liquid with an odd number of components cannot be constructed in a purely 1D lattice system. In a helical liquid with an odd number of components, a uniform gap in the ground state can appear when the time-reversal symmetry is spontaneously broken by interactions. On the other hand, a correlated two-particle backscattering term by an impurity can become relevant while keeping the time-reversal invariance.
We show that the quantum spin Hall (QSH) effect, a state of matter with topological properties distinct from those of conventional insulators, can be realized in mercury telluride-cadmium telluride semiconductor quantum wells. When the thickness of the quantum well is varied, the electronic state changes from a normal to an "inverted" type at a critical thickness d(c). We show that this transition is a topological quantum phase transition between a conventional insulating phase and a phase exhibiting the QSH effect with a single pair of helical edge states. We also discuss methods for experimental detection of the QSH effect.
The stability to interactions and disorder of the quantum spin Hall effect
(QSHE) proposed for time-reversal-invariant 2D systems is discussed. The QSHE
requires an energy gap in the bulk and gapless edge modes that conduct spin-up
and spin-down excitations in opposite directions. When the number of Kramers
pairs of edge modes is odd, certain one-particle scattering processes are
forbidden due to a topological $\mathbb{Z}_2$ index. We show that in a
many-body description, there are other scattering processes that can localize
the edge modes and destroy the QSHE: the region of stability for both classes
of models (even or odd number of Kramers pairs) is obtained explicitly in the
chiral boson theory. For a single Kramers pair the QSHE is stable to weak
interactions and disorder, while for two Kramers pairs it is not; however, the
two-pair case can be stabilized by {\it either} finite attractive or repulsive
interactions. For the simplest case of a single pair of edge modes, it is shown
that changing the screening length in an edge with screened Coulomb
interactions can be used to drive a phase transition between the QSHE state and
the ordinary insulator.
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