A theoretical model is proposed to describe asymmetric gate-voltage dependence of conductance and noise in two-terminal ballistic graphene devices. The model is analyzed independently within the self-consistent Hartree and Thomas-Fermi approximations. Our results justify the prominent role of metal contacts in recent experiments with suspended graphene flakes. The contact-induced electrostatic potentials in graphene demonstrate a power-law decay with the exponent varying from -1 to -0.5. Within our model we explain electron-hole asymmetry and strong Fabri-Perot oscillations of the conductance and noise at positive doping, which were observed in many experiments with submicrometer samples. Limitations of the Thomas-Fermi approximation in a vicinity of the Dirac point are discussed.
We propose three-terminal spin devices with graphene nanoribbons (terminals) and a graphene flake (channel) to generate a highly spin-polarized current without an external magnetic field or ferromagnetic electrodes. The Hubbard repulsion within the mean-field approximation plays the main role to separate the unpolarized electric current at the source terminal into spin-polarized currents at the drain terminals. It is shown that by modulating one of the drain voltages, a fully spin-polarized current can be generated in the other drain terminal. In addition, the geometry of the channel and the a…
We report the investigation of electron transport through a four-terminal graphene-superconductor hybrid system. Due to the quantum interference of the reflected holes from two graphene-superconductor interfaces with phase difference $θ$, it is found that the specular Andreev reflection vanishes at $θ=0$ while the Andreev retroreflection disappears at $θ=π$. This means that the retroreflection and specular reflection can be easily controlled and separated in this device. In addition, due to the diffraction effect in the narrow graphene nanoribbon, the reflected hole can exit from both graphene…
We report room-temperature Coulomb blockade in a single layer graphene three-terminal single-electron transistor (SET) fabricated using feedback-controlled electroburning. The small separation between the side gate electrode and the graphene quantum dot results in a gate coupling up to 3 times larger compared to the value found for the back gate electrode. This allows for an effective tuning between the conductive and Coulomb blocked state using a small side gate voltage of about 1V. The technique can potentially be used in the future to fabricate all-graphene based room temperature single-ele…
This paper is Comment to the Letter "Oscillatory Spin-Filtering due to Gate Control of Spin-Dependent Interface Conductance", by D. Grundler (PRL 86, 1058 (2001)).
Nonlinear electrical properties of graphene-based three-terminal nanojunctions are presented. Intrinsic rectification of voltage is observed up to room temperature. The sign and the efficiency of the rectification can be tuned by a gate. Changing the charge carrier type from holes to electrons results in a change of the rectification sign. At a bias < 20mV and at a temperature below 4.2K the sign and the efficiency of the rectification are governed by universal conductance fluctuations.
Measurement and theory of the two-terminal conductance of monolayer and bilayer graphene in the quantum Hall regime are compared. We examine features of conductance as a function of gate voltage that allow monolayer, bilayer, and gapped samples to be distinguished, including N-shaped distortions of quantum Hall plateaus and conductance peaks and dips at the charge neutrality point. Generally good agreement is found between measurement and theory. Possible origins of discrepancies are discussed.
We introduce a new scheme to realize suspended, multi-terminal graphene structures that can be current annealed successfully to obtain uniform, very high quality devices. A key aspect is that the bulky metallic contacts are not connected directly to the part of graphene probed by transport measurements, but only through etched constriction, which prevents the contacts from acting invasively. The device high quality and uniformity is demonstrated by a reproducibly narrow (delta_n ~ 10^9 cm^-2) resistance peak around charge neutrality, by carrier mobility values exceeding 10^6 cm^2/V/s, by the o…
We investigate the electronic properties of ballistic planar Josephson junctions with multiple superconducting terminals. Our devices consist of monolayer graphene encapsulated in boron nitride with molybdenum-rhenium contacts. Resistance measurements yield multiple resonant features, which are attributed to supercurrent flow among adjacent and non-adjacent Josephson junctions. In particular, we find that superconducting and dissipative currents coexist within the same region of graphene. We show that the presence of dissipative currents primarily results in electron heating and estimate the a…
The characteristics of energy band spectrum of armchair graphene nanoribbons in presence of line defect are analyzed within a simple non-interacting tight-binding framework. In metallic nanoribbons an energy gap may or may not appear in the band spectrum depending on the location of the defect line, while in semiconducting ribbons the gaps are customized, yielding the potential applicabilities of graphene nanoribbons in nanoscale electronic devices. With a more general model, we also investigate two-terminal electron transport using Green's function formalism.
Spin dependent transport in a three-terminal graphene nanoribbon (GNR) is investigated in presence of Rashba spin-orbit interaction. Such a three-terminal structure is shown to be highly effective in filtering electron spins from an unpolarized source simultaneously into two output leads and thus can be used as an efficient spin filter device compared to a two-terminal one. The study of sensitivity of the spin-polarized transmission on the location of the outgoing leads results in interesting consequences and is explored in details. There exist certain symmetry relations between the two outgoi…
Valley-polarized currents can be generated by local straining of multi-terminal graphene devices. The pseudo-magnetic field created by the deformation allows electrons from only one valley to transmit and a current of electrons from a single valley is generated at the opposite side of the locally strained region. We show that valley filtering is most effective with bumps of a certain height and width. Despite the fact that the highest contribution to the polarized current comes from electrons from the lowest sub-band, contributions of other sub-bands are not negligible and can significantly en…
In this paper we describe a graphene p-n junction created by chemical doping. We find that chemical doping does not reduce mobility in contrast to top-gating. The preparation technique has been developed from systematic studies about influences on the initial doping of freshly prepared graphene. We investigated the removal of adsorbates by vacuum treatment, annealing and compensation doping using NH3. Hysteretic behavior is observed in the electric field effect due to dipolar adsorbates like water and NH3. Finally we demonstrate spatially selective doping of graphene using patterned PMMA. 4-te…
Straintronic devices made of carbon-based materials have been pushed up due to the graphene high mechanical flexibility and the possibility of interesting changes in transport properties. Properly designed strained systems have been proposed to allow optimized transport responses that can be explored in experimental realizations. In multi-terminal systems, comparisons between schemes with different geometries are important to characterize the modifications introduced by mechanical deformations, specially if the deformations are localized at a central part of the system or extended in a large r…
Valley filtering processes have been explored in different graphene-based configurations and scenarios to control transport responses. Here we propose graphene multi-terminal set-ups properly designed to obtain valley filtered currents in a broad range of energy, besides the possibility of controlling their directions. We explore graphene systems with extended mechanical fold-like deformations as an opportunity to enhance valley filtered transmission. The mixing between the electronic confinement effects due to a magnetic field and strain results in a selective drive of the current components …
We investigate the transport properties of three-terminal graphene devices, where one terminal is superconducting and two are normal metals. The terminals are connected by nanoribbons. Electron transfer (ET) and crossed Andreev reflection (CAR) are identified via the non-local signal between the two normal terminals. Analytical expressions for ET and CAR in symmetric devices are found. We compute ET and CAR numerically for asymmetric devices. ET dominates CAR in symmetric devices, but CAR can dominate ET in asymmetric devices, where only the zero-energy modes of the zigzag nanoribbons contribu…
Finite bias spectroscopy measurements of a three-terminal graphene quantum dot are presented. Numerous lines of enhanced differential conductance are observed outside the Coulomb diamonds. In the single-level transport regime such lines are often associated with transport through excited states. Here the system is in the multi-level transport regime. We argue that the lines are most likely a result of strong coupling to only a few of the excited states available in the bias window. We also discuss the option that fluctuations of the density of states in the leads are fully or partly responsibl…
Graphene is known to show a significant photo-thermoelectric effect that can exceed its photovoltaic contribution. Here, by utilizing this effect, we demonstrate a photovoltage measurement of cyclotron resonance in a double-back-gated h-BN/graphene/h-BN two-terminal device. A graphite local bottom gate was fabricated in addition to a p-doped Si global back gate. By tuning the two gate voltages, an in-plane graphene junction having an asymmetric carrier-doping profile was created. With the help of this asymmetric structure, the photo-thermoelectric voltage generated in the vicinity of the metal…
Observations of electron-hole asymmetry in transport through graphene devices at high magnetic field challenge prevalent models of the graphene quantum Hall effect. Here, we study this asymmetry both in conventional magnetotransport and in scanning gate microscopy maps measured in an encapsulated graphene constriction. We reveal that the presence of upstream modes and local doping in the vicinity of electrical contacts leads to a totally different picture of topological breakdown for electrons and holes, explaining the observed asymmetry.
We investigate transport in a three-terminal graphene quantum dot. All nine elements of the conductance matrix have been independently measured. In the Coulomb blockade regime accurate measurements of individual conductance resonances reveal slightly different resonance energies depending on which pair of leads is used for probing. Rapid changes in the tunneling coupling between the leads and the dot due to localized states in the constrictions has been excluded by tuning the difference in resonance energies using in-plane gates which couple preferentially to individual constrictions. The inte…
We investigate polyethylene imine and diazonium salts as stable, complementary dopants on graphene. Transport in graphene devices doped with these molecules exhibits asymmetry in electron and hole conductance. The conductance of one carrier is preserved, while the conductance of the other carrier decreases. Simulations based on nonequilibrium Green's function formalism suggest that the origin of this asymmetry is imbalanced carrier injection from the graphene electrodes caused by misalignment of the electrode and channel neutrality points.
We study numerically cross conductances in a four-terminal all-graphene setup. We show that far away from the Dirac point current flows along zigzag directions, giving the possibility to guide the current between terminals using a tunable pn-junction. The device operates as a gate-controlled current switch, and the electronic properties of graphene are crucial for efficient performance.
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.
Bilayer graphene in a perpendicular electric field can host domain walls between regions of reversed field direction or interlayer stacking. The gapless modes propagating along these domain walls, while not strictly topological, nevertheless have interesting physical properties, including valley-momentum locking. A junction where two domain walls intersect forms the analogue of a quantum point contact. We study theoretically the critical behavior of this junction near the pinch-off transition, which is controlled by two separate classes of non-trivial quantum critical points. For strong intera…
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.
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…
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…
Symmetry breaking perturbations in an electronically conducting medium are known to produce Friedel oscillations (FOs) in various physical quantities of an otherwise pristine material. Here we show in a mathematically transparent fashion that FOs in graphene have a strong sublattice asymmetry. As a result, the presence of impurities and/or defects may impact the distinct graphene sublattices very differently. Furthermore, such an asymmetry an be used to explain the recent observations that Nitrogen atoms and dimers are not randomly distributed in graphene but prefer to occupy one of its two di…
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 construct a two-channel scattering model for the triangular network of valley Hall states in interlayer-biased minimally twisted bilayer graphene from symmetry arguments and investigate electronic transport in a four-terminal setup. In the absence of forward scattering, a single phenomenological parameter tunes the network between a triplet of chiral zigzag modes and pseudo-Landau levels. Moreover, the chiral zigzag modes give rise to robust Aharonov-Bohm resonances in the longitudinal conductance in the presence of a perpendicular magnetic field or an in-plane electric field. Interestingly…
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…
We report numerical simulation result of a recently proposed \{P. Bruno, Phys. Rev. Lett {\bf 79}, 4593, (1997)\} approach to perform magnetic scanning tunneling microscopy with a two terminal non-magnetic tip. It is based upon the spin asymmetry effect of the tunneling current between a ferromagnetic surface and a two-terminal non-magnetic tip. The spin asymmetry effect is due to the spin-orbit scattering in the tip. The effect can be viewed as a Mott scattering of tunneling electrons within the tip. To obtain quantitative results we perform numerical simulation within the single band tight b…
We have investigated current-current correlations in a cross-shaped conductor made of graphene ribbons. We measured auto and cross correlations and compared them with the theoretical predictions for ideal diffusive conductors. Our data deviate from these predictions and agreement can be obtained only by adding contributions from occupation-number noise in the central region connecting the arms of the cross. Furthermore, we have determined Hanbury -- Brown and Twiss (HBT) exchange correlations in this system. Contrary to expectations for a cross-shaped diffusive system, we find finite HBT excha…
We study the charge and spin transport in two and four terminal graphene nanoribbons (GNR) decorated with random distribution of magnetic adatoms. The inclusion of the magnetic adatoms generates only the $z$-component of the spin polarized conductance via an exchange bias in the absence of Rashba spin-orbit interaction (SOI), while in presence of Rashba SOI, one is able to create all the three ($x$, $y$ and $z$) components. This has important consequences for possible spintronic applications. The charge conductance shows interesting behaviour near the zero of the Fermi energy. Where in presenc…
By using the real-space Green-Kubo formalism we study numerically the electron transport properties of low-fluorinated graphene. At low temperatures the diffuse transport regime is expected to be prevalent, and we found a pronounced electron-hole asymmetry in electrical conductivity as a result of quasi-resonant scattering on the localized states. For the finite temperatures in the variable-range hopping transport regime the interpretation of numerical results leads to the appearance of local minima and maxima of the resistance near the energies of the localized states. A comparison with the e…
In this study, the Optical conductivity of substitutionary doped graphene is investigated in presence of the Rashba spin orbit coupling (RSOC). Calculations have been performed within the coherent potential approximation (CPA) beyond the Dirac cone approximation. Results of the current study demonstrate that the optical conductivity is increased by increasing the RSOC strength. Meanwhile it was observed that the anisotropy of the band energy results in a considerable anisotropic optical conductivity (AOC) in monolayer graphene. The sign and magnitude of this anisotropic conductivity was shown …
The quantum Hall and longitudinal resistances in multi-terminal ferromagnetic graphene p-n junctions under a perpendicular magnetic field are investigated. In the Hall measurements, the transverse contacts are assumed to be located at p-n interface to avoid the mixing of edge states at the interface and the resulting quantized resistances are then topologically protected. According to the charge carrier type, the resistances in four-terminal p-n junction can be naturally divided into nine different regimes. The symmetric Hall and longitudinal resistances are observed, with lots of new robust q…
We investigate the spin transport and precession in graphene by using the Hanle effect in nonlocal and threeterminal measurement geometries. Identical spin lifetimes, spin diffusion lengths and spin polarizations are observed in graphene devices for both techniques over a wide range of temperatures. The magnitude of the spin signals is well explained by spin transport models. These observations rules out any signal enhancements or additional scattering mechanisms at the interfaces for both geometries. This validates the applicability of both the measurement methods for graphene based spintroni…
Hybridization of topologically distinct quartet modes in three-terminal graphene Josephson junctions
The Pennsylvania State University（宾夕法尼亚州立大学）；National Institute for Materials Science（国立材料研究所）；Université Grenoble-Alpes（格勒诺布尔阿尔卑斯大学）；CNRS（法国国家科学研究中心）；Grenoble INP（格勒诺布尔理工学院）；Institut NEEL（NEEL研究所）
We study all-carbon-hydrogen molecular transistors where zigzag graphene nanoribbons play the role of three metallic electrodes connected to a ring-shaped 18-annulene molecule. Using the nonequilibrium Green function formalism combined with density functional theory, recently extended to multiterminal devices, we show that the proposed nanostructures exhibit exponentially small transmission when the source and drain electrodes are attached in a configuration that ensures destructive interference of electron paths around the ring. The third electrode, functioning either as an attached infinite-…
We propose a directional switching effect in a metallic device. To such end we exploit a graphene-based device with a three-terminal geometry in the presence of a magnetic field. We show that unidirectional charge and valley currents can be controlled by the Fermi energy and the magnetic field direction in the active device. Interestingly, unidirectional transport of charge and valley is generated between two-terminals at the same bias voltage. Furthermore, we quantify the valley depolarization as a function of disorder concentration. Our results open a way for active graphene-based valleytron…
Using ab-initio methods we investigate the possibility of three-terminal graphene "T-junction" devices and show that these all-graphene edge contacts are energetically feasible when the 1D interface itself is free from foreign atoms. We examine the energetics of various junction structures as a function of the atomic scale geometry. Three-terminal equilibrium Green's functions are used to determine the transmission spectrum and contact resistance of the system. We find that the most symmetric structures have a significant binding energy, and we determine the contact resistances in the junction…
We use the non-equilibrium Green function (NEGF) method in the ballistic limit to provide a quantitative description of the conductance of graphene pn junctions - an important building block for graphene electronics devices. In this paper, recent experiments on graphene junctions are explained by a ballistic transport model, but only if the finite junction transition width, Dw, is accounted for. In particular, the experimentally observed anamolous increase in the resistance asymmetry between nn and np junctions under low source/drain charge density conditions is also quantitatively captured by…
Four-terminal resistances, both longitudinal and diagonal, of a locally gated graphene device are measured in the quantum-Hall (QH) regime. In sharp distinction from previous two-terminal studies [J. R. Williams \textit{et al.}, Science {\bf 317}, 638 (2007); B. Özyilmaz \textit{et al.}, Phys. Rev. Lett. {\bf 99}, 166804 (2007)], asymmetric QH resistances are observed, which provide information on reflection as well as transmission of the QH edge states. Most quantized values of resistances are well analyzed by the assumption that all edge states are equally populated. Contrary to the expectat…
By using four-terminal configurations, we investigated the dependence of longitudinal and diagonal resistances of a graphene p-n interface on the quantum-Hall edge-state equilibration position. The resistance of a p-n device in our four-terminal scheme is asymmetric with respect to the zero point where the filling factor ($ν$) of the entire graphene vanishes. This resistance asymmetry is caused by the chiral-direction-dependent change of the equilibration position and leads to a deeper insight into the equilibration process of the quantum-Hall edge states in a bipolar graphene system.
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…
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 calculate the electronic band structure of ABA-stacked trilayer graphene in the presence of external gates, using a self-consistent Hartree approximation to take account of screening. In the absence of a gate potential, there are separate pairs of linear and parabolic bands at low energy. A gate field perpendicular to the layers breaks mirror reflection symmetry with respect to the central layer and hybridizes the linear and parabolic low-energy bands, leaving a chiral Hamiltonian essentially different from that of monolayer or bilayer graphene. Using the self-consistent Born approximation,…
We investigate conductance fluctuations as a function of carrier density $n$ and magnetic field in diffusive mesoscopic samples made from monolayer and bilayer graphene. We show that the fluctuations' correlation energy and field, which are functions of the diffusion coefficient, have fundamentally different variations with $n$, illustrating the contrast between massive and massless carriers. The field dependent fluctuations are nearly independent of $n$, but the $n$-dependent fluctuations are not universal and are largest at the charge neutrality point. We also measure the second order conduc…
We report the observation of the quantized Hall effect in suspended graphene probed with a two-terminal lead geometry. The failure of earlier Hall-bar measurements is discussed and attributed to the placement of voltage probes in mesoscopic samples. New quantized states are found at integer Landau level fillings outside the sequence 2,6,10.., as well as at a fractional filling ν=1/3. Their presence is revealed by plateaus in the two-terminal conductance which appear in magnetic fields as low as 2 Tesla at low temperatures and persist up to 20 Kelvin in 12 Tesla. The excitation gaps, extracted …
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…
Motivated by the very recent fabrication of sub-10-nm-wide semiconducting graphene nanoribbons [X. Li et al., Science 319, 1229 (2008)], whose band gaps extracted from transport measurements were fitted to density functional theory predictions for magnetic ordering along zigzag edges that is responsible for the insulating ground state, we compute current-voltage (I-V) characteristics of finite-length zigzag graphene nanoribbons (ZGNR) attached to metallic contacts. The transport properties of such devices, at source-drain bias voltages beyond the linear response regime, are obtained using the …
We study finite-frequency quantum noise and photon-assisted electron transport through a wide and ballistic graphene sheet sandwiched between two metallic leads. The elementary excitations allow as to examine the differences between effects related to Fabry-Pérot like interferences and signatures caused by correlations of coherently scattered particles in electron- and hole-like parts of the Dirac spectrum. We identify different features in the current-current auto- and cross-correlation spectra and trace them back to the interference patterns of the product of transmission- and reflection amp…
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 …
In this review we highlight recent theoretical and experimental work on sublattice asymmetric doping of impurities in graphene, with a focus on substitutional Nitrogen dopants. It is well known that one current limitation of graphene in regards to its use in electronics is that in its ordinary state it exhibits no band gap. By doping one of its two sublattices preferentially it is possible to not only open such a gap, which can furthermore be tuned through control of the dopant concentration, but in theory produce quasi-ballistic transport of electrons in the undoped sublattice, both important…
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…
Under a magnetic field perpendicular to an monolayer graphene, the existence of a two-dimensional periodic scatter array can not only mix Landau levels of the same valley for displaying split electron-hole Hofstadter-type energy spectra, but also couple two sets of Landau subbands from different valleys in a bilayer graphene. Such a valley mixing effect with a strong scattering strength has been found observable and studied thoroughly in this paper by using a Bloch-wave expansion approach and a projected $2\times 2$ effective Hamiltonian including interlayer effective mass, interlayer coupling…
