We report the observation of the resonant excitation of edge photocurrents in bilayer graphene subjected to terahertz radiation and a magnetic field. The resonantly excited edge photocurrent is observed for both inter-band (at low carrier densities) and intra-band (at high densities) transitions between Landau levels (LL). While the intra-band LL transitions can be traced to the classical cyclotron resonance (CR) and produce strong resonant features, the inter-band-LL resonances have quantum nature and lead to the weaker features in the measured photocurrent spectra. The magnitude and polarization properties of the observed features agree with the semiclassical theory of the intra-band edge photogalvanic effect, including its Shubnikov-de-Haas oscillations at low temperatures.
We measure microwave photocurrent in devices made from InAs/GaInSb bilayers where both insulating bulk state and conducting edge state were observed in the inverted-band regime, consistent with the theoretical prediction for a quantum spin Hall (QSH) insulator. It has been theoretically proposed that microwave photocurrent could be a unique probe in studying the properties of QSH edge states. To distinguish possible photoresponse between bulk state and helical edge state, we prepare Hall bar and Corbino disk from the same wafer. Results show that the Corbino disk samples have a negligible phot…
We report a combined nano-photocurrent and infrared nanoscopy study of twisted bilayer graphene (TBG) enabling access to the local electronic phenomena at length scales as short as 20 nm. We show that the photocurrent changes sign at carrier densities tracking the local superlattice density of states of TBG. We use this property to identify domains of varying local twist angle by local photo-thermoelectric effect. Consistent with the photocurrent study, infrared nano-imaging experiments reveal optical conductivity features dominated by twist-angle dependent interband transitions. Our results p…
Quasi-periodic moiré patterns and their effect on electronic properties of twisted bilayer graphene (TBG) have been intensely studied. At small twist angle $θ$, due to atomic reconstruction, the moiré superlattice morphs into a network of narrow domain walls separating micron-scale AB and BA stacking regions. We use scanning probe photocurrent imaging to resolve nanoscale variations of the Seebeck coefficient occurring at these domain walls. The observed features become enhanced in a range of mid-infrared frequencies where the hexagonal boron nitride (hBN), which we use as a TBG substrate, is …
One of the hallmarks of light-spin interaction in solids is the appearance of photocurrent that depends on the light helicity. Recent studies have shown that helicity dependent photocurrent (HDP) emerges due to light induced spin current and the inverse spin Hall effect of semimetal thin films. We have studied HDP in metal/semimetal bilayers. Compared to Bi single layer films, we find the HDP is enhanced in metal/Bi bilayers. For the bilayers, the sign of HDP under back illumination reverses from that of front illumination. The back illumination photocurrent is the largest for Ag/Bi bilayers a…
We explore the potential of bilayer graphene as a cryogenic microwave photodetector by studying the microwave absorption in fully suspended clean bilayer graphene pn junctions in the frequency range of $1-5$ GHz at a temperature of 8 K. We observe a distinct photocurrent signal if the device is gated into the pn regime, while there is almost no signal for unipolar doping in either the nn or pp regimes. Most surprisingly, the photocurrent strongly peaks when one side of the junction is gated to the Dirac point (charge-neutrality point CNP), while the other remains in a highly doped state. This …
We have studied the circular photogalvanic effect (CPGE) in Cu/Bi bilayers. When a circularly polarized light in the visible range is irradiated to the bilayer from an oblique incidence, we find a photocurrent that depends on the helicity of light. Such photocurrent appears in a direction perpendicular to the light plane of incidence but is absent in the parallel configuration. The helicity dependent photocurrent is significantly reduced for a Bi single layer film and the effect is nearly absent for a Cu single layer film. Conventional interpretation of the CPGE suggests the existence of spin-…
We report on the observation of photogalvanic effects in twisted bilayer graphene (tBLG) with a twist angle of 0.6°. We show that excitation of tBLG bulk causes a photocurrent, whose sign and magnitude are controlled by orientation of the radiation electric field and the photon helicity. The observed photocurrent provides evidence for the reduction of the point group symmetry in low twist-angle tBLG to the lowest possible one. The developed theory shows that the current is formed by asymmetric scattering in gyrotropic tBLG. We also detected the photogalvanic current formed in the vicinity of t…
We investigate intra-Landau-level collective excitations in a bilayer disordered two-dimensional electron system exposed to a perpendicular magnetic field. The energy spectrum is calculated within the random phase approximation by taking into account electron-impurity scattering in the self-consistent Born approximation which includes consistent vertex corrections. Signatures of these bilayer excitations in drag and collective excitation measurements are identified.
Interaction driven integer quantum Hall effects are anticipated in graphene bilayers because of the near-degeneracy of the eight Landau levels which appear near the neutral system Fermi level. We predict that an intra-Landau-level cyclotron resonance signal will appear at some odd-integer filling factors, accompanied by collective modes which are nearly gapless and have approximate $k^{3/2}$ dispersion. We speculate on the possibility of unususal localization physics associated with these modes.
Heterostructures formed between two different van der Waals materials enable interactions and functionalities absent in each component. In this work we show that vicinity to an atomically thin WSe$_2$ sheet dramatically impacts the energies of the symmetry-broken low Landau levels of bilayer graphene, possibly due to screening. We present a systematic study of the magnetic field and electrical displacement field dependences of the Landau level gaps at filling factor $ν$ = 1, 2, 3, and compare to BN encapsulated pristine bilayer graphene. The exchange-dominated energy splitting between the N = …
The zero-energy Landau level of bilayer graphene is shown to be anomalously sharp (delta-function like) against bond disorder as long as the disorder is correlated over a few lattice constants.The robustness of the zero-mode anomaly can be attributed to the preserved chiral symmetry. Unexpectedly, even when we apply a finite potential difference (i.e., an electric field) between the top and the bottom layers, the valley-split $n=0$ Landau levels remain anomalously sharp although they are now shifted away from the zero energy, while the $n=1$ Landau levels exhibit the usual behavior.
We show that topology of the low-energy band structure in bilayer graphene critically depends on mechanical deformations of the crystal which may easily develop in suspended graphene flakes. We describe the Lifshitz transition that takes place in strained bilayers upon splitting the parabollic bands at intermediate energies into several Dirac cones at the energy scale of few meV. Then, we show how this affects the electron Landau level spectra and the quantum Hall effect.
In this work we introduce a low-energy Hamiltonian for single layer and bilayer black phosphorus that describes the electronic states at the vicinity of the gamma point. The model is based on a recently proposed tight-binding description for electron and hole bands close to the Fermi level. We calculate expressions for the Landau level spectrum as function of magnetic field and in the case of bilayer black phosphorus we investigate the effect of an external bias on the electronic band gap. The results showcase the highly anisotropic character of black phosphorus and in particular for bilayer B…
If bilayer graphene is placed in a high perpendicular magnetic field, several quantum Hall plateaus are observed at low enough temperatures. Of these, the $σ_{xy}=4ne^2/h$ sequence ($n\neq0$) is explained by standard Landau quantization, while the other integer plateaus arise due to interactions. The low-energy excitations in both cases are magnetoexcitons, whose dispersion relation depends on single- and many-body effects in a complicated manner. Analyzing the magnetoexciton modes in bilayer graphene, we find that the mixing of different Landau level transitions not only renormalizes them, bu…
We investigate the charge carrier dynamics in bilayer graphene subject to monochromatic laser irradiation within the Landau level quantization regime. Even though the radiation field does not lift the energy degeneracy of the lowest Landau levels (LLs), it nevertheless has a strong effect on the photoinduced pseudospin polarization response for higher LLs ($n\ge2$). Our results show that the photoinduced bandgaps lead to a finite response of the averaged pseudospin polarization with nontrivial oscillating behavior. It is shown that the contribution from these higher LL transitions turns out to…
The effective mass and superfluidity-normal phase transition temperature of magnetoexcitons in topological insulator bilayers are theoretically investigated. The intra-Landau-level Coulomb interaction is treated perturbatively, from which the effective magnetoexciton mass is analytically discussed. The inclusion of inter-Landau-level Coulomb interaction by more exact numerical diagonalization of the Hamiltonian brings out important modifications to magnetoexciton properties, which are specially characterized by prominent reduction in the magnetoexciton effective mass and promotion in the super…
Electronic structure of graphene monolayer-bilayer junction in a magnetic field is studied within an effective-mass approximation. The energy spectrum is characterized by interface Landau levels, i.e., the locally flat bands appearing near the boundary region, resulting in a series of characteristic peaks in the local density of states. Their energies are independent of boundary types such as zigzag or armchair. In the atomic scale, the local density of states shows a Kekulé pattern due to the valley mixing in the armchair boundary, while does not in the zigzag boundary.
In a magnetic field bilayer graphene supports an octet of zero-energy Landau levels with an extra twofold degeneracy in Landau orbitals n=0 and n=1. It is shown that this orbital degeneracy is lifted due to Coulombic quantum fluctuations of the valence band (the Dirac sea); this is a quantum effect analogous to the Lamb shift in the hydrogen atom. A detailed study is made of how these zero-energy levels evolve, with filling, into a variety of pseudo-zero-mode Landau levels in the presence of possible spin and valley breaking and Coulomb interactions, and a comparison is made with experimental …
We obtain analytical expressions for the eigenstates and the Landau level spectrum of biased graphene bilayers in a magnetic field. The calculations are performed in the context of a four-band continuum model and generalize previous approximate results. Solutions are presented for the spectrum as a function of interlayer coupling, the potential difference between the layers and the magnetic field. The explicit expressions allow us to calculate the oscillator strength and the selection rules for electric dipole transitions between the Landau states. Some transitions are significantly shifted in…
The large lattice constant of Moire superlattice formed in twisted bilayer graphene for small twist enables observing the Landau levels splitting into Hofstadter butterflies in energy spectra for moderate magnetic field. This is expected for generic system under homogeneous bias conditions but its robustness against spatial potential fluctuations is left open question. We study the energy structure of twisted bilayer system in dependence of both, the homogeneous magnetic field and the bias voltage applied exclusively in its central part. Although the translational symmetry is broken, the energ…
The electromagnetic response of bilayer graphene in a magnetic field is studied in comparison with that of monolayer graphene. Both types of graphene turn out to be qualitatively quite similar in dielectric and screening characteristics, especially those deriving from vacuum fluctuations, but the effect is generally much more sizable for bilayers. The presence of the zero-(energy-)mode Landau levels is a feature specific to graphene. In bilayers, unlike in monolayers, the effect of the zero-mode levels becomes visible and even dominant in density response as an externally-controllable band gap…
The $E = 0$ octet of bilayer graphene in the filling factor range of -4 < $ν$ < 4 is a fertile playground for many-body phenomena, yet a Landau level diagram is missing due to strong interactions and competing quantum degrees of freedom. We combine measurements and modeling to construct an empirical and quantitative spectrum. The single-particle-like diagram incorporates interaction effects effectively and provides a unified framework to understand the occupation sequence, gap energies and phase transitions observed in the octet. It serves as a new starting point for more sophisticated calcula…
Bilayer graphene in a magnetic field supports eight zero-energy Landau levels, which, as a tunable band gap develops, evolve into two nearly-degenerate quartets separated by the band gap. A close look is made into the properties of such an isolated quartet of pseudo-zero-mode levels at half filling in the presence of an in-plane electric field and the Coulomb interaction. The pseudo-zero-mode levels turn out to support, via orbital mixing, charge carriers with induced electric dipole moment, which lead to characteristic collective excitations, pseudospin waves, with some controllable features;…
Energy versus magnetic field (Hofstadter butterfly diagram) in twisted bilayer graphene is studied theoretically. If we take the usual Landau gauge, we cannot take a finite periodicity even when the magnetic flux through a supercell is a rational number. We show that the \textit{periodic} Landau gauge, which has the periodicity in one direction, makes it possible to obtain the Hofstadter butterfly diagram. Since a supercell can be large, magnetic flux through a supercell normalized by the flux quantum can be a fractional number with a small denominator, even when a magnetic field is not extrem…
DC photoelectrical currents can be generated purely as a non-linear effect in uniform media lacking inversion symmetry without the need for a material junction or bias voltages to drive it, in what is termed photogalvanic effect. These currents are strongly dependent on the polarization state of the radiation, as well as on topological properties of the underlying Fermi surface such as its Berry curvature. In order to study the intrinsic photogalvanic response of gapped graphene (GG), biased bilayer graphene (BBG), and hexagonal boron nitride (hBN), we compute the non-linear current using a pe…
In [Phys. Rev. Lett. vol. 119, p. 133901 (2017)] it was argued that two parallel graphene layers in the presence of electron drift support unstable plasmon modes. Here we show that the predicted plasmon instability is an artifact of errors upon evaluation of graphene polarizability in the presence if electron drift. Crucial role of broken Galilean invariance and spatial dispersion of conductivity for suppression of plasmon instabilities is highlighted.
The stability of the zero-energy Landau levels in bilayer graphene against the chiral symmetric disorder is examined in the presence of the trigonal warping. Based on the tight-binding lattice model with a bond disorder correlated over several lattice constants, it is shown that among the four Landau levels per spin and per valley, two Landau levels exhibit the anomalous sharpness as in the absence of the trigonal warping, while the other two are broadened, yielding split peaks in the density of states. This can be attributed to the fact that the total chirality in each valley is +2 or -2, whi…
Breakdown of the quantum Hall effect (QHE) is commonly associated with an electric field approaching the inter Landau-level (LL) Zener field, ratio of the Landau gap and cyclotron radius. Eluded in semiconducting heterostructures, in spite of extensive investigation, the intrinsic Zener limit is reported here using high-mobility bilayer graphene and high-frequency current noise. We show that collective excitations arising from electron-electron interactions are essential. Beyond a noiseless ballistic QHE regime a large superpoissonian shot noise signals the breakdown via inter-LL scattering. T…
At the low Landau filling factor $(ν)$ termination of the fractional quantum Hall effect (FQHE) series, two-dimensional electron systems (2DESs) exhibit an insulating phase that is understood as a form of pinned Wigner solid. Here we use microwave spectroscopy to probe the transition to the insulator for a wide quantum well (WQW) sample that can support single-layer or bilayer states depending on its overall carrier density, $n$. We find the insulator exhibits a resonance, which is characteristic of a bilayer solid. The resonance also reveals a pair of transitions within the solid, which are n…
Electronic properties of surface areas decoupled from graphite are studied using scanning tunnelling microscopy and spectroscopy. We show that it is possible to identify decoupled graphene monolayer, Bernal bilayer, and Bernal trilayer on graphite surface according to their tunnelling spectra in high magnetic field. The decoupled monolayer and bilayer exhibit Landau quantization of massless and massive Dirac fermions, respectively. The substrate generates a sizable band gap, ~35 meV, in the Bernal bilayer, therefore, the eightfold degenerate Landau level at the charge neutrality point is split…
Bilayer graphene in a magnetic field supports eight zero-energy Landau levels, which, as a tunable band gap develops, split into two nearly-degenerate quartets separated by the band gap. A close look is made into the properties of such an isolated quartet of pseudo-zero-mode levels at half filling in the presence of an in-plane electric field and the Coulomb interaction, with focus on revealing further controllable features in bilayer graphene. The half-filled pseudo-zero-mode levels support, via orbital level mixing, charge carriers with nonzero electric moment, which would lead to field-indu…
We present a theoretical study of the bandstructure and Landau levels in bilayer graphene at low energies in the presence of a transverse magnetic field and Rashba spin-orbit interaction in the regime of negligible trigonal distortion. Within an effective low energy approach (Löwdin partitioning theory) we derive an effective Hamiltonian for bilayer graphene that incorporates the influence of the Zeeman effect, the Rashba spin-orbit interaction, and inclusively, the role of the intrinsic spin-orbit interaction on the same footing. Particular attention is spent to the energy spectrum and Landau…
We review the effect of uniaxial strain on the low-energy electronic dispersion and Landau level structure of bilayer graphene. Based on the tight-binding approach, we derive a strain-induced term in the low-energy Hamiltonian and show how strain affects the low-energy electronic band structure. Depending on the magnitude and direction of applied strain, we identify three regimes of qualitatively different electronic dispersions. We also show that in a weak magnetic field, sufficient strain results in the filling factor ff=+-4 being the most stable in the quantum Hall effect measurement, inste…
We report bilayer-graphene field effect transistors operating as THz broadband photodetectors based on plasma-waves excitation. By employing wide-gate geometries or buried gate configurations, we achieve a responsivity $\sim 1.2V/W (1.3 mA/W)$ and a noise equivalent power $\sim 2\times 10^{-9} W/Hz^{-1/2}$ in the 0.29-0.38 THz range, in photovoltage and photocurrent mode. The potential of this technology for scalability to higher frequencies and the development of flexible devices makes our approach competitive for a future generation of THz detection systems.
Two-component fractional quantum Hall systems are providing a major motivation for a large section of the physics community. Here we study two-component fractional quantum Hall systems in the spin-polarized half-filled lowest Landau level (filling factor 1/2) and second Landau level (filling factor 5/2) with exact diagonalization utilizing both the spherical and torus geometries. The two distinct two-component systems we consider are the true bilayer and effective bilayers (wide-quantum-well). In each model (bilayer and wide-quantum-well) we completely take into account inter-layer tunneling a…
We investigate the contribution of the low-energy electronic excitations towards the Raman spectrum of bilayer graphene for the incoming photon energy Omega >> 1eV. Starting with the four-band tight-binding model, we derive an effective scattering amplitude that can be incorporated into the commonly used two-band approximation. Due to the influence of the high-energy bands, this effective scattering amplitude is different from the contact interaction amplitude obtained within the two-band model alone. We then calculate the spectral density of the inelastic light scattering accompanied by the e…
We theoretically demonstrate that a system formed by two coupled graphene sheets enables a negative damping regime wherein graphene plasmons are pumped by a DC current. This effect is triggered by electrons drifting through one of the graphene sheets and leads to the spontaneous light emission (spasing) and wave instabilities in the mid-infrared range. It is shown that there is a deep link between the drift-induced instabilities and wave instabilities in moving media, as both result from the hybridization of oscillators with oppositely signed frequencies. With a thickness of few nanometers and…
Here we address the concerns of Svintsov and Ryzhii [arXiv:1812.03764] on our article on negative Landau damping in graphene [Phys. Rev. Lett. 119, 133901 (2017)]. We prove that due to the differences between the kinetic and canonical momenta, the conductivity of drift-current biased graphene is ruled by a Galilean transformation when the electron-electron interactions predominate and force the electron gas to move with constant velocity, similar to a moving medium. Furthermore, it is shown that the nonlocal effects in graphene neither preclude a negative Landau damping nor the emergence of in…
The chiral two-dimensional electron gas in Landau levels $\left\vert N\right\vert >0$ of a Bernal-stacked graphene bilayer has a valley-pseudospin Ising quantum Hall ferromagnetic behavior at odd filling factors $ν_{N}=1,3$ of these fourfold degenerate states. At zero interlayer electrical bias, the ground state at these fillings is spin polarized and electrons occupy one valley or the other while a finite electrical bias produces a series of valley pseudospin-flip transitions. In this work, we extend the Ising behavior to chirally-stacked multilayer graphene and discuss the hysteretic behavio…
A magnetic field applied perpendicularly to the chiral two-dimensional electron gas (C2DEG)\ in a Bernal-stacked bilayer graphene quantizes the kinetic energy into a discrete set of Landau levels $N=0,\pm 1,\pm 2,...$ While Landau level $N=0$ is eighfold degenerate, higher Landau levels ($ \left\vert N\right\vert \geq 1$) are fourfold degenerate when counting spin and valley degrees of freedom. In this work, the Hartree-Fock approximation is used to study the phase diagram of the C2DEG at integer fillings $ \widetilde{ν}=1,2,3$ of these higher Landau levels. At these filling factors, the C2DEG…
We study effects of tilted magnetic fields on energy levels in a double-quantum-well (DQW) system, focusing on the coupling of subbands and Landau levels (LLs). The subband-LL coupling induces anticrossings between LLs, manifested directly in the magnetoresistance. The anticrossing gap becomes larger than the spin splitting at the tilting angle $θ\sim 20^\circ $ and larger than the cyclotron energy at $θ\sim 50^\circ $, demonstrating that the subband-LL coupling exerts a strong influence on quantum Hall states even in at a relatively small $θ$ and plays a dominant role for larger $θ$. We also …
Motivated by a recent experiment, we study the microwave-induced photoconductivity of a two-dimensional electron gas arising from intra-Landau-level transitions within a model where the electrons are subject to a unidirectional periodic potential in addition to a weaker impurity potential. With appropriate identifications, our results can be compared to experiment and allow us to explain the sign of the photocurrent, its dependence on magnetic field and microwave frequency as well as the microwave-induced suppression of the Shubnikov-deHaas oscillations.
In two dimensional electron system in magnetic fields such that the Fermi energy lies in high Landau levels and driven by microwave $ac$-field a divergence of the Coulomb screening due to the Ryzhii photocurrent is predicted. A model of magneto-transport with superposition of long range and short range disorders is introduced. In this model the larger is the gradient of the long range potential the smaller is the longitudinal conductivity/resistivity. As a consequence a qualitative theory of the recently discovered zero-resistance states is given.
We present a self-consistent calculation of the interlayer asymmetry in bilayer graphene caused by an applied electric field in magnetic fields. We show how this asymmetry influences the Landau level spectrum in bilayer graphene and the observable inter-Landau level transitions when they are studied as a function of high magnetic field at fixed filling factor as measured experimentally by E.A. Henriksen et al., Phys. Rev. Lett. 100 (2008), 087403. We also analyze the magneto-optical spectra of bilayer flakes in the photon-energy range corresponding to transitions between degenerate and split b…
We study the Landau quantization of the electronic spectrum for graphene bilayers that are rotationally faulted to produce periodic superlattices. Commensurate twisted bilayers exist in two families distinguished by their sublattice exchange parity. We show that these two families exhibit distinct Landau quantized spectra distinguished both by the interlayer coupling of their zero modes and by an amplitude modulation of their spectra at energies above their low energy interlayer coherence scales. These modulations can provide a powerful experimental probe of the magnitude of a weak coherence s…
We report on a tunable - by magnetic field and gate voltage - conversion of terahertz radiation into a dc current in spatially modulated bilayer graphene. We experimentally demonstrate that the underlying physics is related to the so-called ratchet effect. Our key findings are the direct observation of a sharp cyclotron resonance in the photocurrent and the demonstration of two effects caused by electron-electron interaction: the plasmonic splitting of the resonance due to long-range Coulomb coupling and the partial suppression of its second harmonic due to fast interparticle collisions. We de…
Here we show that the Pfaffian state proposed for the $\frac52$ fractional quantum Hall states in conventional two-dimensional electron systems can be readily realized in a bilayer graphene at one of the Landau levels. The properties and stability of the Pfaffian state at this special Landau level strongly depend on the magnetic field strength. The graphene system shows a transition from the incompressible to a compressible state with increasing magnetic field. At a finite magnetic field of ~10 Tesla, the Pfaffian state in bilayer graphene becomes more stable than its counterpart in convention…
Electronic structures and their Landau quantizations in twisted graphene bilayer and trilayer are investigated using scanning tunnelling microscopy and spectroscopy. In the twisted trilayer, the top graphene layer and second layer are AB (Bernal) stacking and there is a stacking misorientation between the second layer and third layer. Both the twisted bilayer and trilayer exhibit two pronounced low-energy van Hove singularities (VHSs) in their spectra. Below the VHSs, the observed Landau level quantization in the twisted bilayer is identical to that of massless Dirac fermion in graphene monola…
In ordinary semiconductor bilayers, exciton condensates appear at total Landau level filling factor $ν_{T}=1$. We predict that similar states will occur in Bernal stacked graphene bilayers at many non-zero integer filling factors. For $ν_{T} = -3,1$ we find that the superfluid density of the exciton condensate vanishes and that a finite-temperature fluctuation induced first order isotropic-smectic phase transition occurs when the layer densities are not balanced. These anomalous properties of bilayer graphene exciton condensates are due to the degeneracy of Landau levels with $n=0$ and $n=1$ o…
In a Bernal-stacked graphene bilayer, an electronic state in Landau level $% N=0$ is described by its guiding-center index $X$ (in the Landau gauge) and by its valley, spin, and orbital indices $ξ=\pm K,σ=\pm 1,$ and $% n=0,1.$ When Coulomb interaction is taken into account, the chiral two-dimensional electron gas (C2DEG) in this system can support a variety of quantum Hall ferromagnetic (QHF)\ ground states where the spins and/or valley pseudospins and/or orbital pseudospins collectively align in space. In this work, we give a comprehensive account of the phase diagram of the C2DEG at integer…
We report on our studies of interacting electrons in bilayer graphene in a magnetic field. We demonstrate that the long range Coulomb interactions between electrons in this material are highly important. We show that in the unbiased bilayer (where both layers are at the same electrostatic potential), the interactions can cause mixing of Landau levels in moderate magnetic fields. For the biased bilayer (when the two layers are at different potentials), we demonstrate that the interactions are responsible for a change in the total spin of the ground state for half-filled Landau levels in the val…
Bilayer graphene provides a unique platform to explore the rich physics in quantum Hall effect. The unusual combination of spin, valley and orbital degeneracy leads to interesting symmetry broken states with electric and magnetic field. Conventional transport measurements like resistance measurements have been performed to probe the different ordered states in bilayer graphene. However, not much work has been done to directly map the energetics of those states in bilayer graphene. Here, we have carried out the magneto capacitance measurements with electric and magnetic field in a hexagonal bor…
We report on our studies of interacting electrons in bilayer graphene in a magnetic field. We demonstrate that the long range Coulomb interactions between electrons in this material are highly important and account for the band asymmetry in recent optical magneto-absorption experiments. We show that in the unbiased bilayer (where both layers are at the same electrostatic potential), the interactions can cause mixing of Landau levels in moderate magnetic fields. For the biased bilayer (when the two layers are at different potentials), we demonstrate that the interactions are responsible for a c…
We propose that the electronic structure of twisted bilayer graphene (TBG) can be understood as Dirac fermions coupled with opposite pseudo magnetic fields generated by the moiré pattern. The two low-energy flat bands from each monolayer valley originate from the two zeroth pseudo Landau levels of Dirac fermions under such opposite effective magnetic fields, which have opposite sublattice polarizations and carry opposite Chern numbers $\pm1$, giving rise to helical edge states in the gaps below and above the low-energy bulk bands near the first magic angle. We argue that small Coulomb interact…
