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Spin relaxation mechanism under high level of nonmagnetic disorder. (a) When scatterings are frequent, an electron suffers from rapid momentum change where the electronic spin does not have time to follow the instantaneous energy eigenstate given by adiabatic perturbation theory. Instead, the electronic spin precesses about the instantaneous energy eigenstate, which serves as an effective magnetic field Beff. (b) Frequent scatterings constantly change the precession axis of spin. During the interval of two consecutive scatterings the spin can only precess for a small angle. (c) The spin ends up doing a random walk on a unit sphere. The more frequent the scatterings are, the less efficient this random walk is, and consequently spin can preserve its original direction for a longer time. (d) The numerical simulation result for spin relaxation time and momentum relaxation time at Fermi level μ=0.13 eV. As expected, when disorder is high, and have an inverse dependence as in the traditional Dyakonov–Perel spin relaxation mechanism. (e) The simulated DC electro-spin susceptibility κyx(0) plotted against the Fermi level μ at different impurity concentrations. The inset is κyx(0) at a fixed Fermi level μ=0.13 eV versus impurity concentration c. It is clear that under high disorder, the accumulated spin density increases with impurity concentration.
Source publication
To date, spin generation in three-dimensional topological insulators (3D TIs)
is primarily modeled as a single-surface phenomenon, happening independently on
top and bottom surfaces. Because this surface charge transport is
Boltzmann-like, the surface spin accumulation is expected to be proportional to
the momentum relaxation time or the inverse of...
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Citations
... [29][30][31] This leads to a spin-polarized current when electrons propagate along the edges. Using this current, a spin reversal can be induced in the adjacent ferromagnetic layer to facilitate a spin manipulation, making the TI an excellent candidate for spintronic devices [32][33][34][35]. In addition, a strong spin-orbit coupling is of vital importance to the inversion of the valence and conduction bands which is a prerequisite for TIs. ...
The thermoelectric effects of ferromagnetic topological insulators with either two-dimensional (2D) circular or one-dimensional (1D) domain wall skyrmions are studied theoretically. It is found that the topological spin-textures play a significant role in the manipulation of spin-dependent thermoelectric properties. In the vicinity of the charge neutrality point, spin Seebeck coefficients possess finite values whose sign and magnitude can be tuned by temperature in spite of vanishing charge Seebeck coefficients. The majority of the effects of circular skyrmions occurs in the edge-state transport regime by generating Fano antiresonances. While the domain wall skyrmion primarily influences the thermoelectric behaviors near the boundary between the edge-state and bulk-state transport regimes with the resonant tunneling mechanism. Both types of skyrmions which function effectively in distinct transport regimes have potential applications in thermoelectrics.
... The spin conductivity of the surface states of topological insulators has been studied previously [24][25][26][27] . Bulk spin conductivity in topological insulators has been calculated using a simplified tight-binding model without taking into account vertex corrections in Ref. 25. Previously, we studied the spin conductivity of the surface states of topological insulators. ...
We study the spin conductivity of the bulk states of three-dimensional topological insulators within Kubo formalism. Spin Hall effect is the generation of the spin current that is perpendicular to the applied voltage. In the case of a three-dimensional topological insulator, applied voltage along $x$ direction generates transverse spin currents along $y$ and $z$ directions with comparable values. We found that a finite non-universal value of the spin conductivity exists in the gapped region due to the inversion of bands. Contribution to the spin conductivity from the vertex corrections enhances the spin conductivity from the filled states. These findings explain the large spin conductivity that has been observed in topological insulators.
... The spin conductivity of the surface states of topological insulators has been studied previously [24][25][26][27]. Bulk spin conductivity in topological insulators has been calculated using a simplified tight-binding model without taking into account vertex corrections in reference [25]. ...
We study the spin conductivity of the bulk states of three-dimensional topological insulators within Kubo formalism. Spin Hall effect is the generation of the spin current that is perpendicular to the applied voltage. In the case of a three-dimensional topological insulator, applied voltage along $x$ direction generates transverse spin currents along $y$ and $z$ directions with comparable values. We found that finite non-universal value of the spin conductivity exists in the gapped region due to the inversion of bands. Contribution to the spin conductivity from the vertex corrections enhances the spin conductivity from the filled states. These findings explain large spin conductivity that has been observed in topological insulators.
... We calculate the spin Hall conductivity of the four compounds (Sb/Bi) 2 (Se/Te) 3 from first principles, that is by solving the Schrödinger equation in the framework of density functional theory and using the solution to calculate the linear response coefficients. Previous theoretical studies on the intrinsic spin Hall conductivity in topological insulators are limited to those of HgTe [22] by using first principles and Bi 1−x Sb x [23] and Bi 2 Se 3 [24,25] by using a tight binding and an effective Hamiltonian. It is worth noting that the calculation of spin Hall conductivity requires integration over the entire Brillouin zone and that all the bands below the Fermi energy contribute toward the spin Hall effect. ...
... Based on first-principles calculations, Eq. (1) has been used to study the spin Hall effect in semiconductors [35][36][37] and heavy metals [38][39][40]. Previous calculations on topological insulators have been performed for HgTe [22] based on first principles and also for Bi 1−x Sb x [23] and Bi 2 Se 3 [24,25] based on a tight binding and an effective Hamiltonian, respectively. However, first-principles calculations of the spin Hall conductivity for (Bi/Sb) 2 (Se/Te) 3 crystals have not been reported previously. ...
The intrinsic spin Hall conductivity of typical topological insulators Sb$_2$Se$_3$, Sb$_2$Te$_3$, Bi$_2$Se$_3$, and Bi$_2$Te$_3$ in the bulk form, is calculated from first-principles by using density functional theory and the linear response theory in a maximally localized Wannier basis. The results show that there is a finite spin Hall conductivity of 100--200 ($\hbar$/2e)(S/cm) in the vicinity of the Fermi energy. Although the resulting values are an order of magnitude smaller than that of heavy metals, they show a comparable spin Hall angle due to their relatively lower longitudinal conductivity. The spin Hall angle for different compounds are then compared to that of recent experiments on topological-insulator/ferromagnet heterostructures. The comparison suggests that the role of the bulk in generating a spin current and consequently a spin torque in magnetization switching applications is comparable to that of the surface including the spin-momentum locked surface states and the Rashba-Edelstein effect at the interface.
... This is 6 orders of magnitude higher than the field-effect mobility determined in our devices (μ = 0.037 m 2 V −1 s −1 ), and 4 orders of magnitude higher than the highest reported mobility in 3D TIs (μ~1 m 2 V −1 s −1 ) [30][31][32] . Note that though the electron backscattering at the surface of a 3D TI is forbidden, scattering into other angles is possible 33,34 , resulting in finite carrier mobility. Therefore, free carrier diffusion does not explain the observation. ...
Excitons are spin integer particles that are predicted to condense into a coherent quantum state at sufficiently low temperature. Here by using photocurrent imaging we report experimental evidence of formation and efficient transport of non-equilibrium excitons in Bi2-xSbxSe3 nanoribbons. The photocurrent distributions are independent of electric field, indicating that photoexcited electrons and holes form excitons. Remarkably, these excitons can transport over hundreds of micrometers along the topological insulator (TI) nanoribbons before recombination at up to 40 K. The macroscopic transport distance, combined with short carrier lifetime obtained from transient photocurrent measurements, indicates an exciton diffusion coefficient at least 36 m2 s−1, which corresponds to a mobility of 6 × 104 m2 V−1 s−1 at 7 K and is four order of magnitude higher than the value reported for free carriers in TIs. The observation of highly dissipationless exciton transport implies the formation of superfluid-like exciton condensate at the surface of TIs. Exciton condensation may emerge at room temperature in topological materials with strong Coulomb interactions and vanishing electron effective mass. Here, Hou et al. report the formation of excitons in Bi2-xSbxSe3 nanoribbons, which can transport over hundreds of micrometres before recombination up to 40 K, further implying exciton condensation.
... Using the magic of a highly conductive coating in terms of disordertolerant surface states that exist in TIs and WSMs can provide additional control in those applications, as, for example, Weyl semimetals thin films or nanostructures exhibiting ultrahigh conductivities [39,40]. Other functionalities could take advantage of very different responses to an applied magnetic field relevant for magnetotransport or differences between spin textures of the Dirac-cone or Fermi-arc states that could allow a temperature control of current-induced surface spin polarization relevant for spintronics [41,42]. ...
Although strong electronic correlations are known to be responsible for some highly unusual behaviors of solids such as metal-insulator transitions, magnetism, and even high-temperature superconductivity, their interplay with recently discovered topological states of matter awaits a full exploration. Here, we use a modern electronic structure method, combining the density functional theory of band electrons with dynamical self-energies of strongly correlated states, to predict that two well-known phases of actinide compound UNiSn, a paramagnetic semiconducting and antiferromagnetic metallic, correspond to topological insulator (TI) and Weyl semimetal (WSM) phases of topological quantum matter. Thus, the famous unconventional insulator-metal transition observed in UNiSn is also a TI-to-WSM transition. Driven by a strong hybridization between U f-electron multiplet transitions and band electrons, multiple energy gaps open up in the single-particle spectrum whose topological physics is revealed using the calculation of Z_{2} invariants in the strongly correlated regime. A simplified physical picture of these phenomena is provided based on a periodic Anderson model of strong correlations and multiple band inversions that occur in this fascinating compound. Studying the topology of interacting electrons reveals interesting opportunities for finding exotic phase transitions in strongly correlated systems.
... 9,10 A new mechanism predicts that moderate surface disorder can induce spin accumulation at the TI surfaces. 11 The topological nature of the band structure leads to a transverse spin current through the bulk and spin accumulation at the surface under an external electric field. 11 Bi 2 Se 3 has been studied as a thermoelectric material 1,12−14 and a near-infrared transparent conductor 15,16 and more recently as a topological insulator. ...
... 11 The topological nature of the band structure leads to a transverse spin current through the bulk and spin accumulation at the surface under an external electric field. 11 Bi 2 Se 3 has been studied as a thermoelectric material 1,12−14 and a near-infrared transparent conductor 15,16 and more recently as a topological insulator. 6,17 Bi 2 Se 3 is of interest because of its simple surface state with a well-defined single Dirac cone and a wide bulk bandgap of 0.3 eV compared with other TIs and thus is most promising to achieve room temperature spintronic devices. ...
Topological insulators (TIs) are a new class of materials that can exhibit robust spin polarizations at the surfaces and have attracted much attention towards spintronic applications. Here, we optimized a solution route to synthesize ultrathin Bi2Se3 and Sb-doped Bi2Se3 nanoplates with a thickness of 6 - 15 nm and an average lateral size around 5 μm, up to a maximum of 10 μm. Solution chemistry provides a way to study TIs with options to manipulate the surface states. We have synthesized Bi2Se3 and Sb-doped Bi2Se3 and characterized single nanoplates. Sb doping is used to suppress the bulk carriers, and an atomic percentage ~6% of Sb is demonstrated by energy dispersive X-ray spectroscopy (EDS). The 2D electron carrier concentration for Sb-doped Bi2Se3 nanoplates is lowered to 5.5 × 1012 cm-2, reducing the concentration by a factor of 3 compared to the undoped Bi2Se3 nanoplate sample with an average 2D carrier concentration of 16 × 1012 cm-2. At 2 K, pronounced ambipolar field effect is observed on the low-carrier-density Sb-doped Bi2Se3 nanoplates, further demonstrating the flexible manipulation of carrier type and concentration for these single-crystal nanoplates. Large out-of-plane magnetoresistance is measured, with a gate tunable phase coherence length.
... Moreover, the topological properties are correlated with the mechanisms of the long-range magnetic order, and this fact influences the Curie temperature [20,27]. Since the impurities might harm the topological properties, and the spin-polarized states at the surfaces usually do not coexist with the bulk magnetism, a generation of the spin-polarized current through the bulk of the TI was proposed [30]. ...
This work presents a topological material based on the graphene nanobelts. It is intrinsically magnetic. The band inversion in this system is partial and anomalous, as it was recently found in the Au-doped graphene and 2D molecular crystal. The metallic edge states with the Chern number equal to 1 exist in the ferro- and antiferromagnetic phase. The edge states become gapless at a small pressure, around 0.87 GPa, applied along the stacking axis. Their dispersions are not symmetric for the spin up and down. The graphene nanobelts are \(\pi\)-stacked with the AB-type, and the zigzag edges are terminated with the O and H atoms at the opposite sides, in the reversed order along the stacking axis. The propagation of the topological edge states is parallel to the O\(\cdots\)H-interaction direction, across the stacked belts.
... This is 6 orders of magnitude higher than the field-effect mobility determined in our devices ( = 0.037 m 2 /(V s)), and 4 orders of magnitude higher than the highest reported mobility in Bi 2 Se 3 ( ~ 1 m 2 /(V s) 25,26 ). Note that though the electron back scattering at the surface of a 3D TI is forbidden, scattering into other angles is possible 27,28 , resulting in finite carrier mobility. ...
Excitons are spin integer particles that are predicted to condense into a coherent quantum state at sufficiently low temperature, and exciton condensates can be realized at much higher temperature than condensates of atoms because of strong Coulomb binding and small mass. Signatures of exciton condensation have been reported in double quantum wells1-4, microcavities5, graphene6, and transition metal dichalcogenides7. Nonetheless, transport of exciton condensates is not yet understood and it is unclear whether an exciton condensate is a superfluid8,9 or an insulating electronic crystal10,11. Topological insulators (TIs) with massless particles and unique spin textures12 have been theoretically predicted13 as a promising platform for achieving exciton condensation. Here we report experimental evidence of excitonic superfluid phase on the surface of three-dimensional (3D) TIs. We unambiguously confirmed that electrons and holes are paired into charge neutral bound states by the electric field independent photocurrent distributions. And we observed a millimetre-long transport distance of these excitons up to 40 K, which strongly suggests dissipationless propagation. The robust macroscopic quantum states achieved with simple device architecture and broadband photoexcitation at relatively high temperature are expected to find novel applications in quantum computations and spintronics.
... The inset contains a high-angle annular dark-field crosssectional image of WTe 2 /Py, indicating the high quality of the layers and sharp interface. The white scale bar is 2 nm from the topological surface states can be understood as a result of the spin Hall effect in the bulk, establishing the bulk boundary correspondence 42 . Given that a Weyl semimetal may be regarded as the limiting case of a topological insulator (with the gap approaching zero) and it usually exhibits strong spin Hall effect 42 , a similar picture also applies here. ...
Spin-orbit torque has recently been intensively investigated for the purposes of manipulating the magnetization in magnetic nano-devices and understanding fundamental physics. Therefore, the search for novel materials or material combinations that exhibit a strong enough spin-torque effect has become one of the top priorities in this field of spintronics. Weyl semimetal, a new topological material that features open Fermi arc with strong spin-orbit coupling and spin-momentum locking effect, is naturally expected to exhibit an enhanced spin-torque effect in magnetic nano-devices. Here we observe a significantly enhanced spin conductivity, which is associated with the field-like torque at low temperatures. The enhancement is obtained in the b-axis WTe2/Py bilayers of nano-devices but not observed in the a-axis of WTe2/Py nano-devices, which can be ascribed to the enhanced spin accumulation by the spin-momentum locking effect of the Fermi arcs of the Weyl semimetal WTe2.
