Bilayer graphene in a magnetic field hosts a variety of ordered phases built from eight Landau levels close in energy to the neutrality point. These levels are characterized by orbital $n=0,1$, valley $ξ=+,-$ and spin $σ=\uparrow,\downarrow$; their relative energies depend strongly on the Coulomb interaction, magnetic field, and interlayer bias. We treat interactions at the Hartree-Fock level, including the effects of metallic gates, layer separation, spatial extent of the $p_z$ orbitals, all Slonczewski-Weiss-McClure tight-binding parameters, and pressure. We obtain the ground state as function of the applied magnetic field, bias, and pressure. The gates, layer separation and extent of the $p_z$ orbitals weaken the Coulomb interaction at different length scales; these effects distort the phase diagram but do not change its topology. However, previously-predicted continuous transitions become discontinuous when all tight-binding parameters are included nonperturbatively. We find that pressure increases the importance of the noninteracting scale with respect to the Coulomb energy, which drives phase transitions to occur at lower fields. This brings two orbitally polarized states not yet predicted or observed into the experimentally accessible region of the phase diagram, in addition to previously-identified valley-, spin-, and partially orbitally polarized states.
We report on transport properties in dual-gated hexagonal boron nitride (hBN)/bilayer-graphene (BLG) superlattices. Here, BLG is nontwisted, i.e., plain. This paper focuses on the charge neutrality point (CNP) for a plain BLG. Under a perpendicular magnetic field, transitions between two insulating phases at the CNP are detected by varying a displacement field with the study on the resistance-temperature characteristics and the magnetoresistance. This work opens avenues for exploring the global phase diagram of the hBN/BLG superlattices beyond the CNP.
We report the experimental observation of strongly enhanced tunneling between graphene bilayers through a WSe$_2$ barrier when the graphene bilayers are populated with carriers of opposite polarity and equal density. The enhanced tunneling increases sharply in strength with decreasing temperature, and the tunneling current exhibits a vertical onset as a function of interlayer voltage at a temperature of 1.5 K. The strongly enhanced tunneling at overall neutrality departs markedly from single-particle model calculations that otherwise match the measured tunneling current-voltage characteristics…
We report on magneto-transport measurements up to 30 T performed on a bilayer graphene Hall bar, enclosed by two thin hexagonal boron nitride flakes. Our high mobility sample exhibits an insulating state at neutrality point which evolves into a metallic phase when a strong in-plane field is applied, as expected for a transition from a canted antiferromagnetic to a ferromagnetic spin ordered phase. For the first time we individuate a temperature-independent crossing in the four-terminal resistance as a function of the total magnetic field, corresponding to the critical point of the transition. …
A graphene sheet partially covered with a bulk superconductor serves as a normal conductor--superconductor (NS) junction, in which electron transport is mainly governed by Andreev reflection (AR). As excess carriers induced over the covered region penetrate into the uncovered region over a screening length, the charge neutrality point (CNP) in the uncovered region shifts only near the NS interface. We theoretically study the electron transport in a bilayer graphene junction taking account of such spatial variation of the CNP in the electron-doped case. When the Fermi level is close to the CNP …
Utilizing the Baym-Kadanoff formalism with the polarization function calculated in the random phase approximation, the dynamics of the $ν=0$ quantum Hall state in bilayer graphene is analyzed. Two phases with nonzero energy gap, the ferromagnetic and layer asymmetric ones, are found. The phase diagram in the plane $(\tildeΔ_0,B)$, where $\tildeΔ_0$ is a top-bottom gates voltage imbalance, is described. It is shown that the energy gap scales linearly, $ΔE\sim 14 B[T]K, with magnetic field.
Using the semiclassical quantum Boltzmann equation (QBE), we numerically calculate the DC transport properties of bilayer graphene near charge neutrality. We find, in contrast to prior discussions, that phonon scattering is crucial even at temperatures below 40K. Nonetheless, electron-electron scattering still dominates over phonon collisions allowing a hydrodynamic approach. We introduce a simple two-fluid hydrodynamic model of electrons and holes interacting via Coulomb drag and compare our results to the full QBE calculation. We show that the two-fluid model produces quantitatively accurate…
We have measured the magneto-resistance of freely suspended high-mobility bilayer graphene. For magnetic fields $B>1$ T we observe the opening of a field induced gap at the charge neutrality point characterized by a diverging resistance. For higher fields the eight-fold degenerated lowest Landau level lifts completely. Both the sequence of this symmetry breaking and the strong transition of the gap-size point to a ferromagnetic nature of the insulating phase developing at the charge neutrality point.
We study electron transport in nanostructures patterned in bilayer graphene patches grown epitaxially on SiC as a function of doping, magnetic field, and temperature. Away from charge neutrality transport is only weakly modulated by changes in carrier concentration induced by a local side-gate. At low n-type doping close to charge neutrality, electron transport resembles that in exfoliated graphene nanoribbons and is well described by tunnelling of single electrons through a network of Coulomb-blockaded islands. Under the influence of an external magnetic field, Coulomb blockade resonances flu…
We report on a fully self-consistent Hartree-Fock calculation of interaction effects on the Moiré flat bands of twisted bilayer graphene, assuming that valley U(1) symmetry is respected. We use realistic band structures and interactions and focus on the charge neutrality point, where experiments have variously reported either insulating or semimetallic behavior. Restricting the search to orders for which the valley U(1) symmetry remains unbroken, we find three types of self-consistent solutions with competitive ground state energy (i) insulators that break $C_2 {\mathcal T}$ symmetry, includin…
High mobility single and few-layer graphene sheets are in many ways attractive as nanoelectronic circuit hosts but lack energy gaps, which are essential to the operation of field-effect transistors. One of the methods used to create gaps in the spectrum of graphene systems is to form long period moire patterns by aligning the graphene and hexagonal boron nitride (h-BN) substrate lattices. Here, we use planar tunneling devices with thin h-BN barriers to obtain direct and accurate tunneling spectroscopy measurements of the energy gaps in single- and bi-layer graphene-h-BN superlattice structures…
We develop a theory of fluctuation-driven phenomena in thermal transport in graphene double-layers. We work in the regime of electron hydrodynamics and focus on the double charge neutrality point. Although at the neutrality point charge transport is decoupled from the hydrodynamic flow, thermal fluctuations of electron density cause both drag and heat transfer between the layers. The thermal transport in the bilayer system is governed by these two phenomena. We express the drag friction coefficient and the interlayer thermal conductivity in terms of the interlayer distance and the intrinsic co…
The transport properties of the two-dimensional system in HgTe-based quantum wells containing simultaneously electrons and holes of low densities are examined. The Hall resistance, as a function of perpendicular magnetic field, reveals an unconventional behavior, different from the classical N-shaped dependence typical for bipolar systems with electron-hole asymmetry. The quantum features of magnetotransport are explained by means of numerical calculation of the Landau level spectrum based on the Kane Hamiltonian. The origin of the quantum Hall plateau σxy = 0 near the charge neutrality point …
We demonstrate that the low-frequency resistance fluctuations, or noise, in bilayer graphene is strongly connected to its band structure, and displays a minimum when the gap between the conduction and valence band is zero. Using double-gated bilayer graphene devices we have tuned the zero gap and charge neutrality points independently, which offers a versatile mechanism to investigate the low-energy band structure, charge localization and screening properties of bilayer graphene.
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.
We present a linear response calculation for twisted bilayer graphene. The calculation is performed for both the continuum and tight-binding models, with the aim of assessing the validity of the former. All qualitatively important features previously reported by us [T. Stauber et al. Phys. Rev. Lett. 120, 046801 (2018)] for the Drude matrix in the continuum model are also present in the tight-binding calculation, with increasing quantitative agreement for decreasing twist angle. These features include the chiral longitudinal magnetic moment associated with plasmonic modes, and the anomalous co…
The low-energy bands of twisted bilayer graphene form Dirac cones with approximate electron-hole symmetry at small rotation angles. These crossings are protected by the emergent symmetries of moiré patterns, conferring a topological character to the bands. Strain accumulated between layers (heterostrain) shifts the Dirac points both in energy and momentum. The overlap of conduction and valence bands favors an excitonic instability of the Fermi surface close to the neutrality point. The spontaneous condensation of electron-hole pairs breaks time reversal symmetry and the separate conservation o…
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…
We present a detailed numerical study of the electronic transport properties of bilayer and trilayer graphene within a framework of single-electron tight-binding model. Various types of disorder are considered, such as resonant (hydrogen) impurities, vacancies, short- or long-range Gaussian random potentials, and Gaussian random nearest neighbor hopping. The algorithms are based on the numerical solution of the time-dependent Schr ödinger equation and applied to calculate the density of states and conductivities (via the Kubo formula) of large samples containing millions of atoms. In the cases…
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;…
We investigate the transport properties of double-gated bilayer graphene nanoribbons at room temperature. The devices were fabricated using conventional CMOS-compatible processes. By analyzing the dependence of the resistance at the charge neutrality point as a function of the electric field applied perpendicular to the graphene surface, we show that a band gap in the density of states opens, reaching an effective value of ~sim50 meV. This demonstrates the potential of bilayer graphene as FET channel material in a conventional CMOS environment.
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…
We analyze the orbital magnetic susceptibility from the band structure of twisted bilayer graphene. Close to charge neutrality, the out-of-plane susceptibility inherits the strong diamagnetic response from graphene. Increasing the doping, a crossover from diamagnetism to paramagnetism is obtained and a logarithmic divergence develops at the van Hove singularity of the Moiré lattice in the first band. The enhanced paramagnetism at the van Hove singularity is stronger for relatively large angle but gets suppressed by the flat spectrum towards the vicinity of the first magic angle. A diverging pa…
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.
We investigate bilayer graphene transport in the presence of electron-hole puddles induced by long-range charged impurities in the environment. We explain the insulating behavior observed in the temperature dependent conductivity of low mobility bilayer graphene using an analytic statistical theory taking into account the non-mean-field nature of transport in the highly inhomogeneous density and potential landscape. We find that the puddles can induce, even far from the charge neutrality point, a coexisting metallic and insulating transport behavior due to the random local activation gap in th…
Nonlocal resistance is studied in a two-dimensional system with a simultaneous presence of electrons and holes in a 20 nm HgTe quantum well. A large nonlocal electric response is found near the charge neutrality point (CNP) in the presence of a perpendicular magnetic field. We attribute the observed nonlocality to the edge state transport via counter propagating chiral modes similar to the quantum spin Hall effect at zero magnetic field and graphene near Landau filling factor $ν=0$
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…
We report a nonsaturating linear magnetoresistance in charge-compensated bilayer graphene in a temperature range from 1.5 to 150 K. The observed linear magnetoresistance disappears away from charge neutrality ruling out the traditional explanation of the effect in terms of the classical random resistor network model. We show that experimental results qualitatively agree with a phenomenological two-fluid model taking into account electron-hole recombination and finite-size sample geometry.
Stacking two graphene layers twisted by the 'magic angle' $θ\approx 1.1^\circ$ generates flat energy bands, which in turn catalyzes various strongly correlated phenomena depending on filling and sample details. At charge neutrality, transport measurements reveal superficially mundane semimetallicity (as expected when correlations are weak) in some samples yet robust insulation in others. We propose that the interplay between interactions and disorder admits either behavior, even when the system is strongly correlated and locally gapped. Specifically, we argue that strong interactions supplemen…
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…
Recent experiments on twisted bilayer graphene (tBG) close to magic angle show that a small relative rotation in a van der Waals heterostructure greatly alters its electronic properties. We consider various scattering mechanisms and show that the carrier transport in tBG is dominated by a combination of charged impurities and acoustic gauge phonons. Charged impurities still dominate at low temperature and densities because of the inability of Dirac fermions to screen long-range Coulomb potentials at charge neutrality; however, the gauge phonons dominate for most of the experimental regime beca…
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 study the electronic transport properties of a dual-gated bilayer graphene nanodevice via first principles calculations. We investigate the electric current as a function of gate length and temperature. Under the action of an external electrical field we show that even for gate lengths up 100 Ang., a non zero current is exhibited. The results can be explained by the presence of a tunneling regime due the remanescent states in the gap. We also discuss the conditions to reach the charge neutrality point in a system free of defects and extrinsic carrier doping.
The Bistritzer-MacDonald continuum model (BM model) describes the low-energy moiré bands for twisted bilayer graphene (TBG) at small twist angles. We derive a generalized continuum model for TBG near any commensurate twist angle, which is characterized by complex interlayer hoppings at commensurate $AA$ stackings (rather than the real hoppings in the BM model), a real interlayer hopping at commensurate $AB/BA$ stackings, and a global energy shift. The complex phases of the $AA$ stacking hoppings and the twist angle together define a single angle parameter $ϕ_0$. We compute the model parameters…
We present an effective (minimal) theory for chiral two-dimensional materials. These materials possess an electro-magnetic coupling without exhibiting a topological gap. As an example, we study the response of doped twisted bilayers, unveiling unusual phenomena in the zero frequency limit. An in-plane magnetic field induces a huge paramagnetic response at the neutrality point and, upon doping, also gives rise to a substantial longitudinal Hall response. The system also accommodates nontrivial longitudinal plasmonic modes which are associated with a longitudinal magnetic moment, thus endowing t…
In mean-field-theory bilayer graphene's massive Dirac fermion model has a family of broken inversion symmetry ground states with charge gaps and flavor dependent spontaneous inter layer charge transfers. We use a lattice Hartree-Fock model to explore some of the physics which controls whether or not this type of broken symmetry state, which can be viewed as a pseudospin ferromagnet, occurs in nature. We find that inversion symmetry is still broken in the lattice model and estimate that transferred areal densities are $\sim 10^{-5}$ electrons per carbon atom, that the associated energy gaps are…
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 polariza…
We discuss twisted bilayer graphene (TBG) based on a theorem of flat band ferromagnetism put forward by Mielke and Tasaki. According to this theorem, ferromagnetism occurs if the single particle density matrix of the flat band states is irreducible and we argue that this result can be applied to the quasi-flat bands of TBG that emerge around the charge-neutrality point for twist angles around the magic angle $θ\sim1.05^\circ$. We show that the density matrix is irreducible in this case, thus predicting a ferromagnetic ground state for neutral TBG ($n=0$). We then show that the theorem can also…
Landau levels and magneto-optics in 30$^\circ$ quasi-periodic twisted bilayer graphene
Graduate School of Information Sciences, Tohoku University（东北大学信息科学研究生院）；Center for Integrated Science and Humanities, Fukushima Medical University（福岛医科大学综合科学与人文中心）；Institute for Solid State Physics, The University of Tokyo（东京大学固体物理研究所）
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…
