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The band structure of monolayer graphene. (a) ARPES spectra of monolayer graphene, showing several slices through the Dirac cone of monolayer graphene. (b) The k z -dependence of photoemission intensity shows a single line, signature of monolayer graphene. (c) The red solid line shows the peak positions of the MDC fits, and the dotted red line represents the linear fit of the dispersion. The position of the Dirac point is slightly above the Fermi level.
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The Landau-Fermi liquid picture for quasiparticles assumes that charge carriers are dressed by many-body interactions, forming one of the fundamental theories of solids. Whether this picture still holds for a semimetal such as graphene at the neutrality point, i.e., when the chemical potential coincides with the Dirac point energy, is one of the lo...
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Citations
... 57 Close to the Dirac (charge neutrality) point, the electron-electron interaction is expected to play an important role in intrinsic graphene, where the graphene Fermi velocity should present an ultraviolet logarithmic divergence due to the coexistence of Fermi points and strong correlation. 58,59 The divergence in the graphene self-energy is present in both Hartree-Fock and higher order theories, regardless of the screened or bare nature of Coulomb force. 59,60 A number of experimental 58,61,62 and computational 57,63 studies report the expected logarithmic renormalization of the graphene Fermi velocity, obtaining quantitative agreement with the theoretical results. ...
... 58,59 The divergence in the graphene self-energy is present in both Hartree-Fock and higher order theories, regardless of the screened or bare nature of Coulomb force. 59,60 A number of experimental 58,61,62 and computational 57,63 studies report the expected logarithmic renormalization of the graphene Fermi velocity, obtaining quantitative agreement with the theoretical results. However, due to the limitations regarding the momentum resolution, the purity of the samples, and residual doping, the scale at which the divergence sets in is difficult to assess. ...
... I and in the bottom panel of Fig. 3, with the error bar shown in gray. The Fermi velocity measured in Ref. [59] is within the error bar of Ref. [70]. The Fermi velocity computed within PPA is 1.18×10 6 m/s, consistent with previously reported GW values, which range from 1.12 to 1.25(5)×10 6 m/s. ...
The GW self-energy may become computationally challenging to evaluate because of frequency and momentum convolutions. These difficulties were recently addressed by the development of the multipole approximation (MPA) and the W-av methods: MPA accurately approximates full-frequency response functions using a small number of poles, while W-av improves the convergence with respect to the k-point sampling in 2D materials. In this work, we (i) present a theoretical scheme to combine them, and (ii) apply the newly developed approach to the paradigmatic case of graphene. Our findings show an excellent agreement of the calculated QP band structure with angle resolved photoemission spectroscopy (ARPES) data. Furthermore, the computational efficiency of MPA and W-av allows us to explore the logarithmic renormalization of the Dirac cone. To this aim, we develop an analytical model, derived from a Dirac Hamiltonian, that we parametrize using ab initio data. The comparison of the models obtained with the plasmon pole approximation (PPA) and MPA results highlights an important role of the dynamical screening in the cone renormalization.
... Optical spectrum can reveal a lot about electronic band structure, quasiparticles [148], and manybody interactions [149] in graphene-based systems. For studying optical absorption properties Moon et al. [150] showed the importance of spectroscopic characteristics in identifying the rotation angle between two layers. ...
Two-dimensional materials with a single or few layers are exciting nano-scale materials that exhibit unprecedented multi-functional properties including optical, electronic, thermal, chemical and mechanical characteristics. A single layer of different 2D materials or a few layers of the same material may not always have the desired application-specific properties to an optimal level. In this context, a new trend has started gaining prominence lately to develop engineered nano-heterostructures by algorithmically stacking multiple layers of single or different 2D materials, wherein each layer could further have individual twisting angles. The enormous possibilities of forming heterostructures through combining a large number of 2D materials with different numbers, stacking sequences and twisting angles have expanded the scope of nano-scale design well beyond considering only a 2D material mono-layer with a specific set of given properties. Magic angle twisted bilayer graphene, a functional variant of van der Waals heterostructures, has created a buzz recently since it achieves unconventional superconductivity and mott insulation at around $1.1^{\circ}$ twist angle. These findings have ignited the interest of researchers to explore a whole new family of 2D heterostructures by introducing twists between layers to tune and enhance various multi-physical properties individually as well as their weighted compound goals. Here we aim to abridge outcomes of the relevant literature concerning twist-dependent physical properties of bilayer graphene and other multi-layered heterostructures, and subsequently highlight their broad-spectrum potential in critical engineering applications. The evolving trends and challenges have been critically analysed along with insightful perspectives on the potential direction of future research.
... An interesting problem is to determine how the fermion velocity is renormalized by the Coulomb interaction. In 1994, Gonzalez et al [15] carried out a first-order renormalization group (RG) analysis of the Coulomb interaction by using the weak-coupling perturbation theory and revealed a logarithmic renormalization of the fermion velocity, described by v ∝ ln (Λ/| p|), where Λ is an ultraviolet cutoff of fermion momentum p. Experiments have observed a logarithmic velocity renormalization [47][48][49], which appears to be qualitatively consistent with first-order RG result. Barnes et al [31] calculated some higher-order (two-loop and three-loop) corrections and concluded that the logarithmic behavior obtained at first-order is qualitatively altered by such corrections, which signals the breakdown of weak-coupling perturbation theory. ...
... The l.h.s. of equation (55) is a little more complicated than that of equation (48). Originally, the bilinear operators j 0 (x), j 1 (x), j 2 (x), and j 012 (x) are defined as products of ψ(x) and ψ(x), which are supposed to be located at the same time-space point x. ...
... In particular, adding EPI to the system does not change the logarithmic | p|-dependence of v( p) in the small-| p| region caused purely by the Coulomb interaction. This result provides a natural explanation of the surprisingly good agreement between the experimental result of v( p) measured in realistic graphene materials [47][48][49] and the theoretical result of v( p) calculated without taking into account the impact of EPI [11,15]. We see from figures 4(a)-(d) that the renormalized velocity v seems to increase abruptly if ϵ → 0 and | p| → 0. As discussed in [11], this is an artifact caused by infrared cutoffs and the logarithmic | p|-dependence of fermion velocity is actually robust in the small-| p| region as the infrared cutoffs of ϵ and | p| decrease. ...
In condensed-matter systems, electrons are subjected to two different interactions under certain conditions. Even if both interactions are weak, it is difficult to perform perturbative calculations due to the complexity caused by the interplay of two interactions. When one or two interactions are strong, ordinary perturbation theory may become invalid. Here we consider undoped graphene as an example and provide a non-perturbative quantum-field-theoretic analysis of the interplay of electron-phonon interaction and Coulomb interaction. We treat these two interactions on an equal footing and derive the exact Dyson-Schwinger integral equation of the full Dirac-fermion propagator. This equation depends on several complicated correlation functions and thus is difficult to handle. Fortunately, we find that these correlation functions obey a number of exact identities, which allows us to prove that the Dyson-Schwinger equation of full fermion propagator is self-closed. After solving this self-closed equation, we obtain the renormalized fermion velocity and show that its energy (momentum) dependence of renormalized fermion velocity is dominantly determined by the electron-phonon (Coulomb) interaction. In particular, the renormalized velocity exhibits a logarithmic momentum dependence and a non-monotonic energy dependence.
... Figure 2a-c display raw image plots near the K point for dopings of − 0.9 ⋅ 10 12 cm −2 , 0.0 ⋅ 10 12 cm −2 , and 1.1 ⋅ 10 12 cm −2 . Already from the raw data one can see that the spectrum in Fig. 2a is linear, and at the neutrality point ( Fig. 2b) the dispersion looks noticeably steeper near E F (= E D ) than at higher binding energies, in agreement with previous reports 32, 33 . The electron-doped spectrum ( Fig. 2c) presents different structure for the valence band than does the spectrum at similar hole doping: the valence band near the Dirac point (black dashed line) is steeper than the valence band in Fig. 2a (red dashed line). ...
... Though this result is in apparent contrast with some reports using E F sensitive probes 40,41 , we note that the real Coulomb interaction strength α can be isolated more reliably from energy states at the Dirac point 35 rather than from states at E F . Indeed, at E F , the band velocity in graphene is modified by several interactions: notably it is enhanced by the long-range electron-electron interactions 33,35 , and reduced by electron-phonon coupling 33,35,43,44 . In contrast, at the Dirac point the electron-phonon interaction becomes negligible due to the diminished density of states [45][46][47] , and the band velocity is solely enhanced by the electron-electron interaction 39,48 . ...
... Though this result is in apparent contrast with some reports using E F sensitive probes 40,41 , we note that the real Coulomb interaction strength α can be isolated more reliably from energy states at the Dirac point 35 rather than from states at E F . Indeed, at E F , the band velocity in graphene is modified by several interactions: notably it is enhanced by the long-range electron-electron interactions 33,35 , and reduced by electron-phonon coupling 33,35,43,44 . In contrast, at the Dirac point the electron-phonon interaction becomes negligible due to the diminished density of states [45][46][47] , and the band velocity is solely enhanced by the electron-electron interaction 39,48 . ...
Electron-hole asymmetry is a fundamental property in solids that can determine the nature of quantum phase transitions and the regime of operation for devices. The observation of electron-hole asymmetry in graphene and recently in twisted graphene and moiré heterostructures has spurred interest into whether it stems from single-particle effects or from correlations, which are core to the emergence of intriguing phases in moiré systems. Here, we report an effective way to access electron-hole asymmetry in 2D materials by directly measuring the quasiparticle self-energy in graphene/Boron Nitride field-effect devices. As the chemical potential moves from the hole to the electron-doped side, we see an increased strength of electronic correlations manifested by an increase in the band velocity and inverse quasiparticle lifetime. These results suggest that electronic correlations intrinsically drive the electron-hole asymmetry in graphene and by leveraging this asymmetry can provide alternative avenues to generate exotic phases in twisted moiré heterostructures.
... Take graphene as an example; a naive dimensional analysis yields α g ¼ α EM =v F ≈ 2.2, adopting a generic Fermi velocity at Dirac cone v F ≈ 10 6 m=s. While recent calculations [62] and measurements [63,64] reported smaller values in between 0.1 and 1 (mostly due to the suppression by Coulomb screening), they are still significantly bigger than α EM . The smallness of v F compared to the speed of light is the most important factor that lowers the bar to reach the relativistic limit. ...
Detectors with low thresholds for electron recoil open a new window to direct searches of sub-GeV dark matter (DM) candidates. In the past decade, many strong limits on DM-electron interactions have been set, but most on the one which is spin-independent (SI) of both dark matter and electron spins. In this work, we study DM-atom scattering through a spin-dependent (SD) interaction at leading order (LO), using well-benchmarked, state-of-the-art atomic many-body calculations. Exclusion limits on the SD DM-electron cross section are derived with data taken from experiments with xenon and germanium detectors at leading sensitivities. In the DM mass range of 0.1–10 GeV, the best limits set by the XENON1T experiment: σe(SD)<10−41–10−40 cm2, are comparable to the ones drawn on DM-neutron and DM-proton at slightly bigger DM masses. The detector’s responses to the LO SD and SI interactions are analyzed. In nonrelativistic limit, a constant ratio between them leads to an indistinguishability of the SD and SI recoil energy spectra. Relativistic calculations however show the scaling starts to break down at a few hundreds of eV, where the spin-orbit effects become sizable. We discuss the prospects of disentangling the SI and SD components in DM-electron interactions via spectral shape measurements, as well as having spin-sensitive experimental signatures without SI backgrounds.
... However, v is found to peak out from the strictly monotonic TB curve at binding energies of ≈ 0.6 eV and, even more prominent, ≈ 1.1 eV. Such renormalizations differ from the gradual changes in band velocity previously observed for graphene in response to its dielectric environment [58,59]. They could instead point towards hybridization with potential interlayer electronic states of Pb, although the latter cannot be readily discerned from the dominant π bands of QFMLG (at least for the available photon energy). ...
Intercalation is an established technique for tailoring the electronic structure of epitaxial graphene. Moreover, it enables the synthesis of otherwise unstable two-dimensional (2D) layers of elements with unique physical properties compared to their bulk versions due to interfacial quantum confinement. In this work, we present uniformly Pb-intercalated quasifreestanding monolayer graphene on SiC, which turns out to be essentially charge neutral with an unprecedented p-type carrier density of only (5.5±2.5)×109 cm−2. Probing the low-energy electronic structure throughout the entire first surface Brillouin zone by means of momentum microscopy, we clearly discern additional bands related to metallic 2D Pb at the interface. Low-energy electron diffraction further reveals a 10×10 Moiré superperiodicity relative to graphene, counterparts of which cannot be directly identified in the available band structure data. Our experiments demonstrate 2D interlayer confinement and associated band structure formation of a heavy-element superconductor, paving the way towards strong spin-orbit coupling effects or even 2D superconductivity at the graphene-SiC interface.
... As highlighted by the red arrows in Fig. 6(c) and the spectral derivative in the inset, an additional kink emerges in the π band after potassium deposition. It is located at ≈ 1.7 eV down from E F , well below the Dirac point, and corresponds to an increase in band velocity by about a factor of 2. Somewhat similar velocity enhancements have previously been reported near charge neutrality only (n ≈ 10 10 cm −2 ), where they can be attributed to emerging electron-electron interactions [81,82]. At n ≈ 10 14 cm −2 , however, graphene offers a fundamentally different landscape for such manybody interactions, precluding any direct analogy. ...
Recently the graphene-SiC interface has emerged as a versatile platform for the epitaxy of otherwise unstable, monoelemental, two-dimensional (2D) layers via intercalation. Intrinsically capped into a van der Waals heterostructure with overhead graphene, they compose a new class of quantum materials with striking properties contrasting their parent bulk crystals. Intercalated silver presents a prototypical example where 2D quantum confinement and inversion symmetry breaking entail a metal-to-semiconductor transition. However, little is known about the associated unoccupied states, and control of the Fermi-level position across the band gap would be desirable. Here, we n-type dope a graphene/2D-Ag/SiC heterostack via in situ potassium deposition and probe its band structure by means of synchrotron-based angle-resolved photoelectron spectroscopy. While the induced carrier densities on the order of 1014cm−2 are not yet sufficient to reach the onset of the silver conduction band, the band alignment of graphene changes relative to the rigidly shifting Ag valence band and substrate core levels. We further demonstrate an ordered potassium adlayer (2×2 relative to graphene) with free-electron-like dispersion, suppressing plasmaron quasiparticles in graphene via enhanced metallization of the heterostack. Our results establish surface charge-transfer doping as an efficient handle to modify band alignment and electronic properties of a van der Waals heterostructure assembled from graphene and a novel type of monolayered quantum material.
... Through the linear fitting according to Eq. (3) in Fig. 6(b), the effective dielectric constant of the dot is yielded as ε ≈ (6.62 ± 0.25)ε 0 . Here ε 0 is the vaccuum dielectric constant [84][85][86][87][88]. On the other hand, the Coulom interaction also breaks the corresponding WGM of the partially filled quasi-bound states [14]. ...
Graphene quantum dots (GQDs) not only have potential applications on spin qubit, but also serve as essential platforms to study the fundamental properties of Dirac fermions, such as Klein tunneling and Berry phase. By now, the study of quantum confinement in GQDs still attract much attention in condensed matter physics. In this article, we review the experimental progresses on quantum confinement in GQDs mainly by using scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS). Here, the GQDs are divided into Klein GQDs, bound-state GQDs and edge-terminated GQDs according to their different confinement strength. Based on the realization of quasi-bound states in Klein GQDs, external perpendicular magnetic field is utilized as a manipulation approach to trigger and control the novel properties by tuning Berry phase and electron-electron (e-e) interaction. The tip-induced edge-free GQDs can serve as an intuitive mean to explore the broken symmetry states at nanoscale and single-electron accuracy, which are expected to be used in studying physical properties of different two-dimensional materials. Moreover, high-spin magnetic ground states are successfully introduced in edge-terminated GQDs by designing and synthesizing triangulene zigzag nanographenes.
... However, v is found to peak out from the strictly monotonic TB curve at binding energies of ≈ 0.6 eV and, even more prominent, ≈ 1.1 eV. Such renormalizations differ from the gradual changes in band velocity previously observed for graphene in response to its dielectric environment [57,58]. They could instead point towards hybridization with potential interlayer electronic states of Pb, although the latter cannot be readily discerned from the dominant π bands of QFMLG (at least for the available photon energy). ...
Intercalation is an established technique for tailoring the electronic structure of epitaxial graphene. Moreover, it enables the synthesis of otherwise unstable two-dimensional (2D) layers of elements with unique physical properties compared to their bulk versions due to interfacial quantum confinement. In this work, we present uniformly Pb-intercalated quasi-freestanding monolayer graphene on SiC, which turns out to be essentially charge neutral with an unprecedented $p$-type carrier density of only $(5.5\pm2.5)\times10^9$ cm$^{-2}$. Probing the low-energy electronic structure throughout the entire first surface Brillouin zone by means of momentum microscopy, we clearly discern additional bands related to metallic 2D-Pb at the interface. Low-energy electron diffraction further reveals a $10\times10$ Moir\'e superperiodicity relative to graphene, counterparts of which cannot be directly identified in the available band structure data. Our experiments demonstrate 2D interlayer confinement and associated band structure formation of a heavy-element superconductor, paving the way towards strong spin-orbit coupling effects or even 2D superconductivity at the graphene/SiC interface.
... Note finally the emergence of an additional kink in the π band after potassium deposition as highlighted by the red arrows in Fig. 6(c) and the spectral derivative in the inset. It is located at ≈ 1.7 eV down from E F , well below the Dirac point, and corresponds to an increase in band velocity by about a factor of 2. Somewhat similar velocity enhancements have previously been reported near charge neutrality only (n ≈ 10 10 cm −2 ), where they can be attributed to emerging electron-electron interactions 70,71 . At n ≈ 10 14 cm −2 however, graphene offers a fundamentally different landscape for such many-body interactions, precluding any direct analogy. ...
Recently the graphene/SiC interface has emerged as a versatile platform for the epitaxy of otherwise unstable, monoelemental, two-dimensional (2D) layers via intercalation. Intrinsically capped into a van der Waals heterostructure with overhead graphene, they compose a new class of quantum materials with striking properties contrasting their parent bulk crystals. Intercalated silver presents a prototypical example where 2D quantum confinement and inversion symmetry breaking entail a metal-to-semiconductor transition. However, little is known about the associated unoccupied states and coherent control of the Fermi level position across the bandgap would be desirable. Here, we n-type dope a graphene/2D-Ag/SiC heterostack via in situ potassium deposition and probe its band structure by means of synchrotron-based angle-resolved photoelectron spectroscopy. While the induced carrier densities on the order of $10^{14}$ cm$^{-2}$ are not yet sufficient to reach the onset of the silver conduction band, the band alignment of graphene can be tuned relative to the rigidly shifting Ag valence band and substrate core levels. We further demonstrate an ordered potassium adlayer ($2\times 2$ relative to graphene) with free-electron-like dispersion, suppressing plasmaron quasiparticles in graphene via enhanced metalization of the heterostack. Our results establish surface charge-transfer doping as an efficient handle to tune band alignment and electronic properties of a van der Waals heterostructure assembled from graphene and a novel type of monolayered quantum material.
