When a bilayer of graphene is placed in a suitably configured field effect device, an asymmetry gap can be generated and the carrier concentration made different in each layer. This provides a tunable semiconducting gap, and the valence and the conductance band no longer meet at the two Dirac points of the graphene Brillouin zone. We calculate the optical conductivity of such a semiconductor with particular emphasis on the optical spectral weight redistribution brought about by changes in gap and chemical potential due to charging. We derive an algebraic formula for arbitrary value of the chemical potential for the case of the bilayer conductivity without a gap.
We address the optical conductivity of undoped bilayer graphene in the presence of a finite bias voltage at finite temperature. The effects of gap parameter and stacking type on optical conductivity are discussed in the context of tight binding model Hamiltonian. Green's function approach has been implemented to find the behavior of optical conductivity of bilayer graphene within linear response theory. We have found the frequency dependence of optical conductivity for different values of gap parameter and bias voltage. Also the dependence of optical conductivity on the temperature has been in…
We calculate the optical sum associated with the in-plane conductivity of a graphene bilayer. A bilayer asymmetry gap generated in a field-effect device can split apart valence and conduction bands, which otherwise would meet at two K points in the Brillouin zone. In this way one can go from a compensated semimetal to a semiconductor with a tunable gap. However, the sum rule turns out to be 'protected' against the opening of this semiconducting gap, in contrast to the large variations observed in other systems where the gap is induced by strong correlation effects.
Bilayer graphene (BLG) at the charge neutrality point (CNP) is strongly susceptible to electronic interactions, and expected to undergo a phase transition into a state with spontaneous broken symmetries. By systematically investigating a large number of singly- and doubly-gated bilayer graphene (BLG) devices, we show that an insulating state appears only in devices with high mobility and low extrinsic doping. This insulating state has an associated transition temperature Tc~5K and an energy gap of ~3 meV, thus strongly suggesting a gapped broken symmetry state that is destroyed by very weak di…
We report precision measurements of the effective mass m* in high-quality bilayer graphene using the temperature dependence of the Shubnikov-de Haas oscillations. In the density range of 0.7 x 10^12/cm^2 < n < 4.1 x 10^12 /cm^2, both the hole mass m*_h and the electron mass m*_e increase with increasing density, demonstrating the hyperbolic nature of the bands. The hole mass m*_h is approximately 20-30% larger than the electron mass m*_e. Tight-binding calculations provide a good description of the electron-hole asymmetry and yield an accurate measure of the inter-layer hopping parameter v_4 =…
Using the Landauer formula approach, it is proven that minimal conductivity of order of $e^{2}/h$ found experimentally in bilayer graphene is its intrinsic property. For the case of ideal crystals, the conductivity turns our to be equal to $e^{2}/2h$ per valley per spin. A zero-temperature shot noise in bilayer graphene is considered and the Fano factor is calculated. Its value $1-2/π$ is close to the value 1/3 found earlier for the single-layer graphene.
We report precision measurements of the effective mass m* in high-quality bilayer graphene using the temperature dependence of the Shubnikov-de Haas oscillations. In the density range of 0.7 x 10^12/cm^2 < n < 4.1 x 10^12 /cm^2, both the hole mass m*_h and the electron mass m*_e increase with increasing density, demonstrating the hyperbolic nature of the bands. The hole mass m*_h is approximately 20-30% larger than the electron mass m*_e. Tight-binding calculations provide a good description of the electron-hole asymmetry and yield an accurate measure of the inter-layer hopping parameter v_4 =…
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 consider the time-reversal odd dynamics of the bilayer graphene at low energies in the quantum Hall regime. A generating functional for the effective action that captures the electromagnetic response to all orders in momentum and frequency is presented and evaluated to the third order in the space-time gradient $\mathcal O(\partial^3)$. In addition, we calculate the Hall viscosity and derive an explicit relationship with the $q^2$ coefficient of the Hall conductivity. It is reminiscent of the Hoyos--Son relation in the Galilean invariant systems, which can be recovered in the limit of large…
We present a theory of the influence of band renormalization and excitonic electron-electron interaction effects on the optical conductivity $σ(ω)$ of doped bilayer graphene. Using the Keldysh formalism, we derive a kinetic equation from which we extract numerical and approximate analytic results for $σ(ω)$. Our calculations reveal a previously unrecognized mechanism which couples the Drude and interband response and renormalizes the plasmon frequency, and suggest that screening must play an essential role in explaining the weakly renormalized conductivity seen in recent experiments.
We report on study of low-energy excitations in a bilayer hetero-structure 2D electron gas. We split the bilayer Hamiltonian into SU(4)-symmetric part and the anisotropy part and treat the latter as a perturbation. We find that both Goldstone and the charged excitations - skyrmions - are goverened by the non-linear Sigma Model. We calculate the anisotropic energy gap of the skyrmion to have a prominent minimum in the canted antiferromagnetic phase of bilayer. We compare our findings with the results of recent experiments.
We reported the basal-plane thermal conductivity in exfoliated bilayer hexagonal boron nitride h-BN that was measured using suspended prepatterned microstructures. The h-BN sample suitable for thermal measurements was fabricated by dry-transfer method, whose sample quality, due to less polymer residues on surfaces, is believed to be superior to that of PMMA-mediated samples. The measured room temperature thermal conductivity is around 484 Wm-1K-1(+141 Wm-1K-1/ -24 Wm-1K-1) which exceeds that in bulk h-BN, providing experimental observation of the thickness-dependent thermal conductivity in sus…
A Drude-Boltzmann theory is used to calculate the transport properties of bilayer graphene. We find that for typical carrier densities accessible in graphene experiments, the dominant scattering mechanism is overscreened Coulomb impurities that behave like short-range scatterers. We anticipate that the conductivity $σ(n)$ is linear in $n$ at high density and has a plateau at low density corresponding to a residual density of $n^* = \sqrt{n_{\rm imp} {\tilde n}}$, where ${\tilde n}$ is a constant which we estimate using a self-consistent Thomas-Fermi screening approximation to be ${\tilde n} \a…
Inter-Landau-level transitions in the bilayer graphene at high perpendicular magnetic field at the filling-factor v<<1 have been studied. The next-nearest-neighbor transitions, energy difference between dimer and non-dimer sites and layer asymmetry are included. The influence of Coulomb interaction is taken into account. The magnetoplasmon excitations in bilayer graphene at small momenta are considered in the frame of the Hartree-Fock approximation. It is shown that asymmetry in cyclotron resonance of clean bilayer graphene depends on magnetic field. At lower magnetic fields the energy splitti…
In this paper, we study the quantum properties of a bilayer graphene with (asymmetry) line defects. The localized states are found around the line defects. Thus, the line defects on one certain layer of the bilayer graphene can lead to an electric transport channel. By adding a bias potential along the direction of the line defects, we calculate the electric conductivity of bilayer graphene with line defects using Landauer-Büttiker theory, and show that the channel affects the electric conductivity remarkably by comparing the results with those in a perfect bilayer graphene. This one-dimension…
The gapless energy band spectra make the structures based on graphene and graphene bilayers with the population inversion created by optical or injection pumping to be promising media for the interband terahertz (THz) lasing. However, a strong intraband absorption at THz frequencies still poses a challenge for efficient THz lasing. In this paper, we show that in the pumped graphene bilayer structures, the indirect interband radiative transitions accompanied by scattering of carriers caused by disorder can provide a substantial negative contribution to the THz conductivity (together with the di…
The in-plane DC conductivity of twisted bilayer graphene (TBLG) is calculated using an expansion of the real-space Kubo-Bastin conductivity in terms of Chebyshev polynomials. We investigate within a tight-binding (TB) approach the transport properties as a function of rotation angle, applied perpendicular electric field and vacancy disorder. We find that for high-angle twists, the two layers are effectively decoupled, and the minimum conductivity at the Dirac point corresponds to double the value observed in monolayer graphene. This remains valid even in the presence of vacancies, hinting that…
We numerically calculate the optical conductivity of twisted graphene bilayers within the continuum model. To obtain the imaginary part, we employ the regularized Kramers-Kronig relation allowing us to discuss arbitrary twist angles, chemical potential and temperature. We find that the Drude weight $D$ as function of the chemical potential $μ$ closely follows the shell structure of twisted bilayer displayed by the density of states. For certain angles, this results in a transport gap D=0 at finite $μ$. We also discuss the loss function which, for low doping, is characterized by acoustic interb…
We study the superlattice minibands produced by the interplay between moiré pattern induced by hexagonal BN substrate on graphene layer and the interlayer coupling in bilayer graphene with Bernal stacking (BLG). We compare moiré miniband features in BLG, where they are affected by the interlayer asymmetry of BLG-hBN heterostructure and trigonal warping characteristic for electrons in Bernal-stacked bilayers with those found in monolayer graphene.
We report on infrared spectroscopy of bilayer graphene integrated in gated structures. We observed a significant asymmetry in the optical conductivity upon electrostatic doping of electrons and holes. We show that this finding arises from a marked asymmetry between the valence and conduction bands, which is mainly due to the inequivalence of the two sublattices within the graphene layer. From the conductivity data, the energy difference of the two sublattices is determined.
This is a theoretical study of electron transport in gated bilayer graphene - a novel semiconducting material with a tunable band gap. It is shown that the which-layer pseudospin coherence enhances the subgap conductivity and facilitates the thermally activated transport. The mechanism proposed can also lead to the non-monotonic conductivity vs. temperature dependence at a band gap size of the order of 10 meV. The effect can be observed in gapped bilayer graphene sandwiched in boron nitride where the electron-hole puddles and flexural phonons are strongly suppressed.
We present a mechamism why interlayer tunneling conductivity in coherent bilayer quantum Hall states at $ν=1$ is anomalously large, but finite in the recent experiment. According to the mechanism, pseudoSkyrmions causes the finite conductivity, although there exists an expectation that dissipationless tunneling current arises in the state. PseudoSkyrmions have an intrinsic polarization field perpendicular to the layers, which causes the dissipation. Using the mechanism we show that the large peak in the conductivity remains for weak parallel magnetic field, but decay rapidly after its strength…
Assuming diffusive carrier transport and employing an effective medium theory, we calculate the temperature dependence of bilayer graphene conductivity due to Fermi-surface broadening as a function of carrier density. We find that the temperature dependence of the conductivity depends strongly on the amount of disorder. In the regime relevant to most experiments, the conductivity is a function of T/T*, where T* is the characteristic temperature set by disorder. We demonstrate that experimental data taken from various groups collapse onto a theoretically predicted scaling function.
The mechanisms of optical activity and quantum transport of twisted bilayer graphene are studied. The formation of unique electron states in the bilayer systems is studied using an effective continuum model. Such states are shown to support the correlation of transverse motions of electrons in two graphene layers. Because of the chiral structure of the atomic lattices, the contribution of such drag correlations is incompletely cancelled, thus resulting in a drag term of the optical conductivity tensor. We show that the drag term of the conductivity is the manifestation of the spatial dispersio…
Moiré systems displaying flat bands have emerged as novel platforms to study correlated electron phenomena. Insulating and superconducting states appear upon doping magic angle twisted bilayer graphene (TBG), and there is evidence of correlation induced effects at the charge neutrality point (CNP) which could originate from spontaneous symmetry breaking. Our theoretical calculations show how optical conductivity measurements can distinguish different symmetry breaking states, and reveal the nature of the correlated states. In the specific case of nematic order, which breaks the discrete rotati…
We calculated the minimal longitudinal conductivity in prefect single and bilayer graphene by extending the two methods developed for Dirac fermion gas by A. W. W. Ludwig et al. in Phys. Rev. B {\bf 50}, 7526 (1994). Using the Kubo formula which was originally applied for spintronic systems we obtain $σ^{\text min}_{xx}= (J π/2) e^2/h$ while from the other formula used in the above mentioned work we find $\barσ^{\text min}_{xx}= (4J/π) e^2/h$, where J=1 for single layer and J=2 for bilayer graphene. The two universal values are different although they are numerically close to each other. Our t…
We present a theoretical study of the effects of heterostrain and lattice relaxation on the optical conductivity of twisted bilayer graphene near the magic angle, based on the band structures obtained from a continuum model. We find that heterostrain, lattice relaxation and their combination give rise to very distinctive spectroscopic features in the optical conductivity, which can be used to probe and distinguish these effects. From the spectrum at various Fermi energies, important features in the strain- and relaxation-modified band structure such as the bandgap, bandwidth and van Hove singu…
Cyclotron resonance in bilayer graphene is studied with weak electron-hole asymmetry, suggested by experiment, taken into account and with the focus on many-body corrections that evade Kohn's theorem. It is shown by direct calculation that the theory remains renormalizable to O(e^2) in the presence of electron-hole asymmetry parameters, and a general program to carry out renormalization for graphene under a magnetic field is presented. Inclusion of electron-hole asymmetry in part improves the theoretical fit to the existing data and the data appear to indicate the running of the renormalized v…
Fermi line of bilayer graphene at zero energy is transformed into four separated points positioned trigonally at the corner of the hexagonal first Brillouin zone. We show that as a result of this trigonal splitting the minimal conductivity of an undoped bilayer graphene strip becomes anisotropic with respect to the orientation $θ$ of the connected electrodes and finds a dependence on its length $L$ on the characteristic scale $\ell=π/Δk\simeq 50 nm$ determined by the inverse of k-space distance of two Dirac points. The minimum conductivity increases from a universal isotropic value $σ^{min}_{\…
We study the optical response of bilayer graphene with a kink potential composed of a domain wall separating two AB regions with opposite interlayer bias. The band structure and the local optical conductivity in real space are investigated in details based on a continuum model. We find that the one-dimensional chiral states localized at the domain wall contribute significantly to the local optical conductivity, which shows a clear distinction in different regions. The effects of domain wall states on optical conductivity can be detected by spatially and frequency resolved spectroscopic feature…
Injection or optical generation of electrons and holes in graphene bilayers (GBLs) can result in the interband population inversion enabling the terahertz (THz) radiation lasing. The intraband radiative processes compete with the interband transitions. We demonstrate that remote doping enhances the indirect interband generation of photons in the proposed GBL heterostructures. Therefore such remote doping helps surpassing the intraband (Drude) absorption and results in large absolute values of the negative dynamic THz conductivity in a wide range of frequencies at elevated (including room) temp…
Using a reformulated Kubo formula we calculate the zero-energy minimal conductivity of bilayer graphene taking into account the small but finite trigonal warping. We find that the conductivity is independent of the strength of the trigonal warping and it is three times as large as that without trigonal warping, and six times larger than that in single layer graphene. Although the trigonal warping of the dispersion relation around the valleys in the Brillouin zone is effective only for low energy excitations, our result shows that its role cannot be neglected in the zero-energy minimal conducti…
We derive analytical expressions for the conductivity of bilayer graphene (BLG) using the Boltzmann approach within the the Born approximation for a model of Gaussian disorders describing both short- and long-range impurity scattering. The range of validity of the Born approximation is established by comparing the analytical results to exact tight-binding numerical calculations. A comparison of the obtained density dependencies of the conductivity with experimental data shows that the BLG samples investigated experimentally so far are in the quantum scattering regime where the Fermi wavelength…
We show that a coherent picture of the dc conductivity of monolayer and bilayer graphene at finite electronic densities emerges upon considering that strong short-range potentials are the main source of scattering in these two systems. The origin of the strong short-range potentials may lie in adsorbed hydrocarbons at the surface of graphene. The equivalence among results based on the partial-wave description of scattering, the Lippmann-Schwinger equation, and the T-matrix approach is established. Scattering due to resonant impurities close to the neutrality point is investigated via a numeric…
We calculate the dynamical conductivity of AA-stacked bilayer graphene as a function of frequency and in the presence of a finite chemical potential due to charging. Unlike the monolayer, we find a Drude absorption at charge neutrality in addition to an interband absorption with onset of twice the interlayer hopping energy. At finite doping, the interband absorption exhibits two edges which depend on both chemical potential and interlayer hopping energy. We study the behaviour as a function of varying chemical potential relative to the interlayer hopping energy scale and compute the partial op…
We study the ballistic conductivity of graphene bilayer in the presence of next-nearest neighbor hoppings between the layers. An undoped and unbiased system was found in Ref. [1] to show a nonuniversal (length-dependent) conductivity $σ(L)$, approaching the value of $σ_\star=3/π\simeq{}0.95$ for large $L$. Here we demonstrate one-parameter scaling and determine the scaling function $β(σ)=d\ln{}\!σ/d\ln{}\!L$. The scaling flow has an attractive fixed point [$\,β(σ_\star)=0$, $β'(σ_\star)<0\,$] reproducing the scenario predicted for random impurity scattering of Dirac fermions with Coulomb repul…
Using the Kubo formula we develop a general and simple expression for the minimal conductivity in systems described by a two by two Hamiltonian. As an application we derive an analytical expression for the minimal conductivity tensor of bilayer graphene as a function of a complex parameter $w$ related to recently proposed symmetry breaking mechanisms resulting from electron-electron interaction or strain applied to the sample. The number of Dirac points changes with varying parameter w, this directly affect the minimal conductivity. Our analytic expression is confirmed using an independent cal…
Recent experiments have reported evidence of dominant electron-hole scattering in the electric conductivity of suspended bilayer graphene near charge neutrality. According to these experiments, plots of the electric conductivity as a function of $μ/k_BT$ (chemical potential scaled with temperature) obtained for different temperatures in the range of $12\rm{K}\lesssim T \lesssim 40\rm{K}$ collapse on a single curve independent of $T$. In a recent theory, this observation has been taken as an indication that the main sub-dominant scattering process is not electron-impurity but electron-phonon. H…
We theoretically study the band structure and optical conductivity of twisted bilayer graphene (TBG) near the magic angle considering the effects of lattice relaxation. We show that the optical conductivity spectrum is characterized by a series of peaks associated with the van Hove singularities in the band structure, and the peak energies evolve systematically with the twist angle. Lattice relaxation effects in TBG modify its band structure, especially the flat bands, which lead to significant shifts of the peaks in optical conductivity. These results demonstrate that spectroscopic features i…
A tight binding model is used to calculate the band structure of bilayer graphene in the presence of a potential difference between the layers that opens a gap $Δ$ between the conduction and valence bands. In particular, a self consistent Hartree approximation is used to describe imperfect screening of an external gate, employed primarily to control the density $n$ of electrons on the bilayer, resulting in a potential difference between the layers and a density dependent gap $Δ(n)$. We discuss the influence of a finite asymmetry gap $Δ(0)$ at zero excess density, caused by the screening of an …
We have surveyed the in-plane transport properties of the graphene twist bilayer using (i) a low-energy effective Hamiltonian for the underlying electronic structure, (ii) an isotropic elastic phonon model, and (iii) the linear Boltzmann equation for elastic electron-phonon scattering. We find that transport in the twist bilayer is profoundly sensitive to the rotation angle of the constituent layers. Similar to the electronic structure of the twist bilayer the transport is qualitatively different in three distinct angle regimes. At large angles ($θ> \,\approx\!\!10^\circ$) and at temperatures …
We calculate the finite-frequency conductivity of bilayer graphene with a relative twist between the layers. The low frequency response at zero doping shows a flat conductivity with value twice that of the monolayer case and at higher frequency a strong absorption peak occurs. For finite doping, the low frequency flat absorption is modified into a peak about zero frequency (the Drude response) accompanied by an interband edge which results from the transfer of spectral weight from interband to intraband absorption due to Pauli blocking. If the system is doped sufficiently such that the chemica…
Using the method developed in the companion paper, we construct the effective continuum theories for two different microscopic tight binding models of the twisted bilayer graphene at the twist angle of $1.05^\circ$, one Slater-Koster based and the other ab-initio Wannier based. The energy spectra obtained from the continuum theory -- either for rigid twist or including lattice relaxation -- are found to be in nearly perfect agreement with the spectra from the tight binding models when the gradient expansion is carried out to second order, demonstrating the validity of the method. We also analy…
Boltzmann transport theory fails near the linear band-crossing of single-layer graphene and near the quadratic band-crossing of bilayer graphene. We report on a numerical study which assesses the role of inter-band coherence in transport when the Fermi level lies near the band-crossing energy of bilayer graphene. We find that interband coherence enhances conduction, and that it plays an essential role in graphene's minimum conductivity phenomena. This behavior is qualitatively captured by an approximate theory which treats inter-band coherence in a relaxation-time approximation. On the basis o…
We show that Friedel charge oscillation near an interface opens a gap at the Fermi energy for electrons with wave vectors perpendicular to the interface. If the Friedel gaps on two sides of the interface are different, a nonequlibrium effect - shifting of these gaps under bias - leads to asymmetric transport upon reversing the bias polarity. The predicted transport asymmetry is revealed by scanning tunneling potentiometry at monolayer-bilayer interfaces in epitaxial graphene on SiC (0001). This intriguing interfacial transport behavior opens a new avenue towards novel quantum functions such as…
Intrinsic bilayer graphene is a gapless semimetal. Under the application of a bias field it becomes a semiconductor with a direct band gap that is proportional to the applied field. Under a layer-asymmetric strain (where the upper layer undergoes compression and lower layer tension or visa-versa) we find that the band gap of a biased bilayer graphene ribbon becomes indirect and, for higher strains, becomes negative returning the material its original semimetal state. As a result, the conductivity of the ribbon increases and can be almost an order of magnitude larger that of the intrinsic unbia…
We report a systematic study of the optical conductivity of twisted bilayer graphene (tBLG) across a large energy range (1.2 eV to 5.6 eV) for various twist angles, combined with first-principles calculations. At previously unexplored high energies, our data show signatures of multiple van Hove singularities (vHSs) in the tBLG bands, as well as the nonlinearity of the single layer graphene bands and their electron-hole asymmetry. Our data also suggest that excitonic effects play a vital role in the optical spectra of tBLG. Including electron-hole interactions in first-principles calculations i…
We consider a double-layer system made of two parallel bilayer graphene sheets separated by a dielectric medium. We calculate the finite-temperature electrical conductivity of the first layer due to charged impurities located in two layers. We study the effects of temperature, interlayer distance, dielectric constants and impurity concentration, carrier concentration on the electrical conductivity. We show the importance of charged impurities located in layer II in determining electrical conductivity of the first layer for small interlayer distance. The results in this paper give us more under…
A transformation of the band structure in bilayer graphene (BLG) with relatively shifted layers has been studied in the framework of the tight-binding model. BLG is demonstrated to remain a zero-gap material in the whole range of experimentally attainable shifts, but the positions of contact points between the conduction and valence bands depend substantially on the shift direction. The shift results in a considerable anisotropy of the band spectrum, which is, in turn, responsible for a substantial (10-20%) anisotropy of the conductivity in BLG. A possibility of using this anisotropy in high-s…
We study the effects of disorder on bilayer graphene using four different microscopic models and directly compare their results. We compute the self-energy, density of states, and optical conductivity in the presence of short-ranged scatterers and screened Coulomb impurities, using both the Born approximation and self-consistent Born approximation for the self-energy. We also include a finite interlayer potential asymmetry which generates a gap between the valence and conduction bands. We find that the qualitative behavior of the two scattering potentials are similar, but that the choice of ap…
We report an experimental study of temperature-dependent spectral lineshapes of phonon side-band emission stemming from dark excitons in monolayer and bilayer WSe$_{2}$. Using photoluminescence spectroscopy in the range from 4 to 100K, we observe a pronounced asymmetry in the phonon-assisted luminescence from momentum-indirect exciton reservoirs. We demonstrate that the corresponding spectral profiles are distinct from those of bright excitons with direct radiative decay pathways. The lineshape asymmetry reflects thermal distribution of exciton states with finite center-of-mass momenta, charac…
We investigate the band structure and the optical absorption spectrum of twisted bilayer graphenes with changing interlayer bias and Fermi energy simultaneously. We show that the interlayer bias lifts the degeneracy of the superlattice Dirac point, while the amount of the Dirac point shift is significantly suppressed in small rotation angles, and even becomes opposite to the applied bias. We calculate the optical absorption spectrum in various asymmetric potentials and Fermi energies, and associate the characteristic spectral features with the band structure. The spectroscopic features are hig…
We have performed a theoretical study of electronic transport in single and bilayer graphene based on the standard linear-response (Kubo) formalism and continuum-model descriptions of the graphene band structure. We are focusing especially on the interband contribution to the optical conductivity. Analytical results are obtained for a variety of situations, which allow clear identification of features in the conductivity that are associated with relevant electronic energy scales. Our work extends previous numerical studies and elucidates ways to infer electronic properties of graphene samples …
Cascades in transport and optical conductivity of Twisted Bilayer Graphene
Instituto de Ciencia de Materiales de Madrid (ICMM), CSIC（马德里材料科学研究所，西班牙国家研究委员会）；Ciclo Básico Común, Universidad de Buenos Aires and IFIBA, Conicet（布宜诺斯艾利斯大学基础课程部及IFIBA，阿根廷国家科学研究委员会）；Université de Paris, Laboratoire Matériaux et Phénomènes Quantiques, CNRS（巴黎大学物质与量子现象实验室，法国国家科学研究中心）；Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides（巴黎萨克雷大学，法国国家科学研究中心，固体物理实验室）；Aalto University School of Science（阿尔托大学理学院）
We derive an effective Hamiltonian at low energies for bilayer graphene when Fermi velocity manufactured on each layer is different of the velocity measured in pristine graphene. Based on the effective Hamiltonian, we investigate the influence of Fermi velocity asymmetry on the band structure of trigonally warped bilayer graphene in the presence of interlayer applied bias. In this case, the Fermi line at low energies is still preserved its threefold rotational symmetry appearing as the three pockets. Furthermore, the interlayer asymmetry in Fermi velocities leads to an indirect band gap which …
The electronic and optical response of Bernal stacked bilayer graphene with geometry modulation and gate voltage are studied. The broken symmetry in sublattices, one dimensional periodicity perpendicular to the domain wall and out-of-plane axis introduces substantial changes of wavefunctions, such as gapless topological protected states, standing waves with bonding and anti-bonding characteristics, rich structures in density of states and optical spectra. The wavefunctions present well-behaved standing waves in pure system and complicated node structures in geometry-modulated system. The optic…
