The role of electron-electron interactions in two-dimensional Dirac fermions

Tang, Ho-Kin; Leaw, Jia Ning; Rodrigues, J. N. B.; Herbut, Igor F.; Sengupta, Pinaki; Assaad, Fakher F.; Adam, Shaffique

doi:10.1126/science.aao2934

Cited by 114 publications

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“…(b) The renormalization group flows in Ref. (1) were most strongly influenced by the logarithmic divergence (at finite γ) of ∆v F (k) at large momenta, and as such, the numerical value of ∆v F at γ = 0, U = U c and k → 0 is not germane to our paper. Actually we did not even claim in the paper to be the first to calculate it.…”

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confidence: 77%

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“…4 The stability of QH states at higher temperature suggests that the LL bands remain robust up to 50 K. Therefore, the large response of Et with temperature in the lowest LL states could arise from a different origin such as mid-gap impurity states in TI surfaces 35 or possibly developing interacting states which are correlated with our smaller v F . 36 This suggests that capacitance is more sensitive to the gap states in 3D TI compared to transport. Higher quality BSTS devices with significant reduction in disorder are required to resolve the extra features in these LLs.…”

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Landau Levels of Topologically-Protected Surface States Probed by Dual-Gated Quantum Capacitance

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Spectroscopy of discrete Landau levels (LLs) in bulk-insulating three-dimensional topological insulators (3D TIs) in perpendicular magnetic field characterizes the Dirac nature of their surface states. Despite a number of studies demonstrating the quantum Hall effect (QHE) of topological surface states, quantitative evaluation of the LL energies, which serve as fundamental electronic quantities for study of the quantum states, is still limited. In this work, we explore the density of states of LLs by measuring quantum capacitance (CQ) in a truly bulk insulating 3D TI via a van der Waals heterostructure configuration. By applying dual gate voltages, we access the individual surface states' LLs and extract their chemical potentials to quantify the LL spacings of each 2 surface. We evaluate the LLs' energies at two distinguished QH states, namely dissipationless (ν= ±1) and dissipative (ν= 0) states in the 3D TI. KEYWORDStopological insulators, quantum capacitance, Landau levels, van der Waals heterostructures, quantum Hall effect The topologically-protected linearly dispersing surface states of three-dimensional topological insulators (3D TIs) offer a route for exploration of quantum phenomena such as the topological exciton superfluid, fractional charges and Majorana fermions in quantum regimes. 1-3 In a strong perpendicular magnetic field, the surface Dirac fermions localize in cyclotron orbits, forming discrete energy states known as Landau levels (LLs). This gives rise to the quantum Hall effect (QHE) in magnetotransport, where the Hall conductivity is quantized at integers as a result of halfintegers from each (top and bottom) surface. 4-6 Alternatively, quantum capacitance (CQ) can also be exploited to study the LLs electronically. 7-10 Different from quantum transport which is only sensitive to edge modes, CQ provides a probe of the charge states in the bulk of the surfaces. CQ is an ideal measure of the thermodynamic density of states (DoS) for low carrier density and gate-tunable materials. 8-10 Nevertheless, it is relatively less explored in 3D TIs in the past as compared to quantum transport primarily due to the shortcoming of a proper 3D TI candidate.Previous studies of CQ in Bi2Se3 revealed the Dirac-like surface states 11 and Shubnikov-de Haaslike quantum oscillations in magnetic field. 12 However, Bi2Se3 is known to exhibit substantial carrier doping in bulk, and extra trapped states induced by intrinsic defects. 11,13 More recently, CQ in high mobility 3D TI based on strained HgTe was reported, 14 showing more intrinsic bulk band and clear LL quantization. Yet, the narrow bulk bandgap in strained HgTe (~20 meV), which is

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“…However, as shown in Ref. 23, in the realistic system where the long-range interactions are weaker than the contact interactions, the long-range interactions will stabilize the Fermi liquid instead of destabilizing it. One way to understand this is that the long-range interactions favor the charge-density-wave phase, which competes with the antiferromagnetic tendency favored by the contact interaction 24 .…”

Section: Introductionmentioning

confidence: 87%

“…2a. We perform this analysis for various values of t ⊥ , and compare with the monolayer results 23 .…”

Section: Phase Transition Of Bilayer Graphenementioning

confidence: 99%

Electronic ground state in bilayer graphene with realistic Coulomb interactions

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Both insulating and conducting electronic behaviors have been experimentally seen in clean bilayer graphene samples at low temperature, and there is still no consensus on the nature of the interacting ground state at half-filling and in the absence of a magnetic field. Theoretically, several possibilities for the insulating ground states have been predicted for weak interaction strength. However, a recent renormalization-group calculation on a Hubbard model for charge-neutral bilayer graphene with short-range interactions suggests the emergence of low-energy Dirac fermions that would stabilize the metallic phase for weak interactions. Using a non-perturbative projective quantum Monte Carlo, we calculate the ground state for bilayer graphene using a realistic model for the Coulomb interaction that includes both short-range and long-range contributions. We find that a finite critical onsite interaction is needed to gap bilayer graphene, thereby confirming the Hubbard model expectations even in the presence of a long-range Coulomb potential, in agreement with our theoretical renormalization group analysis. In addition, we also find that the critical onsite interactions necessary to destabilize the metallic ground state decreases with increasing interlayer coupling.arXiv:1903.06177v1 [cond-mat.str-el]

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The role of electron-electron interactions in two-dimensional Dirac fermions

Cited by 114 publications

References 44 publications

Response to Comment on “The role of electron-electron interactions in two-dimensional Dirac fermions”

Response to Comment on “The role of electron-electron interactions in two-dimensional Dirac fermions”

Landau Levels of Topologically-Protected Surface States Probed by Dual-Gated Quantum Capacitance

Electronic ground state in bilayer graphene with realistic Coulomb interactions

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