Igor F. Herbut
It is shown that in the absence of spontaneous symmetry breaking the Dirac cones in the system of interacting electrons on honeycomb lattice are isotropic at low energies. The effect is due to the $Z_3$ subgroup of the $D_3$ symmetry group of the dispersion relation of Dirac quasiparticles. Consequences of the violations of the $Z_3$ or the sublattice symmetry are discussed.
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We show that hydrodynamic collision processes of graphene at the neutrality point can be described in terms of a Fokker-Planck equation with fractional derivative, corresponding to a Lévy flight in momentum space. Thus, electron-electron collisions give rise to frequent small-angle scattering processes that are interrupted by rare large-angle events. The latter give rise to superdiffusive dynamics of collective excitations. We argue that such superdiffusive dynamics is of more general importance to the out-of-equilibrium dynamics of quantum-critical systems.
We investigate a generalized two-dimensional Weyl Hamiltonian, which may describe the low-energy properties of mechanically deformed graphene and of the organic compound alpha-(BEDT-TTF)_2I_3 under pressure. The associated dispersion has generically the form of tilted anisotropic Dirac cones. The tilt arises due to next-nearest-neighbor hopping when the Dirac points, where the valence band touches the conduction band, do not coincide with crystallographic high-symmetry points within the first Brillouin zone. Within a semiclassical treatment, we describe the formation of Landau levels in a stro…
We study the spin transport phenomena in two-dimensional graphene-like materials with arbitrary tilted Dirac cones. The tilt arises due to next-nearest hopping when the bottom of the conduction band and top of the valence band does not simultaneously coincide at Dirac point. We consider normal-ferromagnetic-normal (N-F-N) junction of the materials and using the generalized scattering approach calculate the spin current. Here, we show that tilting the Dirac cones can strongly change the transport properties by modifying the period of oscillation of the spin current. The spin conductance can be …
Recently, the existence of Dirac/Weyl cones in three dimensional systems has been demonstrated experimentally. While in high energy physics the isotropy of the Dirac/Weyl cones is guaranteed by relativistic invariance, in condensed matter systems corrections to this can occur, one possible type being a tilt. In this paper we study the effect of of tilted Weyl cones in collective effects. We study both the opticql conductivity as well as the polarization function. We also investigate the perturbative effect of long-range Coulomb interactions using a renormalization group calculation. We find th…
Probing the tunable multi-cone bandstructure in Bernal bilayer graphene
研究利用Landau能级作为能量色散标记，在Bernal双层石墨烯中探测并证实了四个不同的微型Dirac锥，绘制了电位移场诱导的复杂拓扑相变，为石墨烯电子学提供了新工具。
We show that the modulation of the hopping amplitudes in the honeycomb lattice of the monolayer graphene uniquely defines a metric which corresponds to the shape of the Dirac cone. The spin connection of this effective metric field can be obtained from the microscopic tight-binding Hamiltonian exactly, completing the analogy between the sublattice pseudospin travelling in the monolayer graphene with ripples and strain fields, and the real spin $1/2$ fermion travelling in a curved space. The effective metric as seen by the sublattice pseudospin is different from the real space metric as defined…
We report measurements of the cyclotron mass in graphene for carrier concentrations n varying over three orders of magnitude. In contrast to the single-particle picture, the real spectrum of graphene is profoundly nonlinear so that the Fermi velocity describing the spectral slope reaches ~3x10^6 m/s at n <10^10 cm^-2, three times the value commonly used for graphene. The observed changes are attributed to electron-electron interaction that renormalizes the Dirac spectrum because of weak screening. Our experiments also put an upper limit of ~0.1 meV on the possible gap in graphene.
We compute the dynamical polarizability of graphene beyond the usual Dirac cone approximation, integrating over the full Brillouin zone. We find deviations at $\hbarω=2t$ ($t$ the hopping parameter) which amount to a logarithmic singularity due to the van Hove singularity and derive an approximate analytical expression. Also at low energies, we find deviations from the results obtained from the Dirac cone approximation which manifest themselves in a peak spitting at arbitrary direction of the incoming wave vector $\q$. Consequences for the plasmon spectrum are discussed.
The Dirac electrons of graphene, an intrinsic zero gap semiconductor, uniquely carry spin and pseudospin that give rise to many fascinating electronic and transport properties. While isolated zigzag graphene nanoribbons are antiferromagnetic semiconductors, we show by means of first-principles and tight-binding calculations that zigzag graphene nanoribbons supported on graphene are half-metallic as a result of spin- and pseudospin-symmetry breaking. In particular, half-metallic Dirac cones are formed at K (K') near the Fermi level. The present results demonstrate that the unique combination of…
Using first principles pseudopotential density functional theory calculations, we find that terminating zigzag graphene nanoribbons (ZGNR) with monovalent alkali atoms at a reduced concentration has a dramatic impact on their properties. In particular, using sodium atoms for the saturation of ZGNR edges at half the concentration of edge-carbon atoms make it a one dimensional, perfect semimetal, where the valance and conduction bands meet at only a single, Dirac-like point. Unlike pristine graphene, the Dirac-"cones" of Na-ZGNR is not symmetric with respect to wave vector, but rather it is tilt…
We investigate the quantum tunneling of electrons in an AA-stacked bilayer graphene (BLG) $n$-$p$ junction and $n$-$p$-$n$ junction. We show that Klein tunneling of an electron can occur in this system. The quasiparticles are not only chiral but are additionally described by a `cone index'. Due to the orthogonality of states with different cone indexes, electron transport across a potential barrier must strictly conserve the cone index and this leads to the protected cone transport which is unique in AA-stacked BLG. Together with the negative refraction of electrons, electrons residing in diff…
Anisotropic Dirac cones can appear in a number of correlated electron systems, such as cuprate superconductors and deformed graphene. We study the influence of long-range Coulomb interaction on the physical properties of an anisotropic graphene by using the renormalization group method and 1/N expansion, where N is the flavor of Dirac fermions. Our explicit calculations reveal that the anisotropic fermion velocities flow monotonously to an isotropic fixed point in the lowest energy limit in clean graphene. We then incorporate three sorts of disorders, including random chemical potential, rando…
We study the electronic structures of ABA (Bernal) stacked multilayer graphenes in uniform perpendicular electric field, and show that the interplay of the trigonal warping and the potential asymmetry gives rise to a number of emergent Dirac cones nearly touching at zero energy. The band velocity and the energy region (typically a few tens of meV) of these gate-induced Dirac cones are tunable with the external electric field. In ABA trilayer graphene, in particular, applying an electric field induces a non-trivial valley Hall state, where the energy gap at the Dirac point is filled by chiral e…
The fluctuations of the electromagnetic vacuum are one of the most powerful manifestations of the quantum structure of nature. Their effect on the Dirac electrons of graphene is known to induce some spectacular and purely quantistic phenomena, like the Casimir and the Aharanov--Bohm effects. In this work we demonstrate, by using a first principles approach, that the Dirac cone of graphene is also affected by a sizable Lamb shift.We show that the microscopic electronic currents flowing on the graphene plane couple efficiently with the vacuum fluctuations causing a renormalization of the electro…
Graphene flakes placed on hexagonal boron nitride feature in the presence of a magnetic field a complex electronic structure due to a hexagonal moiré potential resulting from the van der Waals interaction with the substrate. The slight lattice mismatch gives rise to a periodic supercell potential. Zone folding is expected to create replica of the original Dirac cone and Hofstadter butterflies. Our large-scale tight binding simulation reveals an unexpected coexistence of a relativistic and non-relativistic Landau level structure. The presence of the zeroth Landau level and its associated butter…
Electrons in quantum materials exhibiting coexistence of dispersionless (flat) bands piercing dispersive (steep) bands can give rise to strongly correlated phenomena, and are associated with unconventional superconductivity. It is known that in twisted trilayer graphene steep Dirac cones can coexist with band flattening, but the phenomenon is not stable under layer misalignments. Here we show that such a twisted sandwiched graphene (TSWG) -- a three-layer van der Waals heterostructure with a twisted middle layer -- can have very stable flat bands coexisting with Dirac cones near the Fermi ener…
We investigate generation of new Dirac cones in graphene under double-periodic and quasiperiodic superlattice potentials. We first show that double-periodic potentials generate the Dirac cones sporadically, following the Diophantine equation, in spite of the fact that double-periodic potentials are also periodic ones, for which previous studies predict consecutive appearance of the cones. The sporadic appearance is due to the fact that the dispersion relation of graphene is linear only up to an energy cutoff. We then show that quasiperiodic potentials generate the new Dirac cones densely with …
Designer gapped and tilted Dirac cones in lateral graphene superlattices
通过双极波导阵列调控石墨烯中狄拉克锥的间隙和倾斜，利用超晶格紧束缚模型和转移矩阵计算验证，通过栅极电压调节实现太赫兹频段的狄拉克锥调控，为太赫兹应用提供新方法。
The quantum Hall effect in graphene is regarded to be involving half-integer topological numbers associated with the massless Dirac particle, this is usually not apparent due to the doubling of the Dirac cones. Here we theoretically consider two classes of lattice models in which we manipulate the Dirac cones with either (a) two Dirac points that have mutually different energies, or (b) multiple Dirac cones having different Fermi velocities. We have shown, with an explicit calculation of the topological (Chern) number for case (a) and with an adiabatic argument for case (b) that the results ar…
Massless Dirac fermions occur as low-energy modes in several quasi-two-dimensional condensed matter systems such as graphene, the surface of bulk topological insulators, and in layered organic semiconductors. When the rotational symmetry in such systems is reduced either by an in-plane electric field or an intrinsic tilt of the Dirac cones, the allowed dipolar optical transitions evolve from a few selected transitions into a wide fan of interband transitions. We show that the Lorentz covariance of the low-energy carriers allows for a concise analysis of the emerging magneto-optical properties.…
Cone-dependent retro and specular Andreev reflections in AA-stacked bilayer graphene
本研究理论探究AA堆叠双层石墨烯/超导体结的Andreev反射，发现其依赖锥自由度，可通过层间电势调控反射类型，实现不同锥载流子的空间分离与电导分别测量。
A quantum graph model for a single sheet of graphene is extended to bilayer and trilayer Bernal-stacked graphene; the spectra are characterized and the dispersion relations explicitly obtained; Dirac cones are then proven to be present only for trilayer graphene, although the bilayer has a gapless parabolic band component. Our model rigorously exhibits basic facts from tight-binding calculations, effective two-dimensional models and a $π$-orbital continuum model with nearest-neighbour tunneling that have been discussed in the physics literature.
We present a two-band model based on periodic Hückel theory, which is capable of predicting the existence and position of Dirac cones in the first Brillouin zone of an infinite class of two-dimensional periodic carbon networks, obtained by systematic perturbation of the graphene connectivity by bond decoration, that is by inclusion of arbitrary $π$-electron Hückel networks into each of the three carbon-carbon $π$-bonds within the graphene unit cell. The bond decoration process can fundamentally modify the graphene unit cell and honeycomb connectivity, representing a simple and general way to d…
Mechanical graphene, which is a spring-mass model with the honeycomb structure, is investigated. The vibration spectrum is dramatically changed by controlling only one parameter, spring tension at equilibrium. In the spectrum, there always exist Dirac cones at K- and K'-points. As the tension is modified, extra Dirac cones are created and annihilated in pairs. When the time reversal symmetry is broken by uniform rotation of the system, creation and annihilation of the Dirac cones result in a jump of the appropriately defined Chern number. Then, a flip of the propagation direction of the chiral…
Non-trivial Berry phase of graphene leads to unusual quantum correction to the conductivity. Berry phase of pi in single layer graphene (SLG) and 2pi in bi-layer graphene (BLG) is expected to reveal weak anti-localization (WAL) and weak localization (WL), respectively. However, experimentally both WAL and WL have been observed in graphene devices depending on the strength of different scattering mechanisms. Graphene superlattice having multiple Dirac cones is expected to exhibit pi to 2pi Berry phase transition from primary Dirac cone (PDC) to cloned Dirac cone (CDC). However, its effect on lo…
The opening of a gap in single-layer graphene is often ascribed to the breaking of the equivalence between the two carbon sublattices. We show by angle-resolved photoemission spectroscopy that Ir- and Na-modified graphene grown on the Ir(111) surface presents a very large unconventional gap that can be described in terms of a phenomenological "massless" Dirac model. We discuss the consequences and differences of this model in comparison of the standard massive gap model, and we investigate the conditions under which such anomalous gap can arise from a spontaneous symmetry breaking.
We study the Friedel oscillations induced by a localized impurity in anisotropic graphene. We focus on the limit when the two inequivalent Dirac points merge. We find that in this limit the Friedel oscillations manifest very peculiar features, such as a strong asymmetry and an atypical inverse square-root decay. Our calculations are performed using both a T-matrix approximation and a tight-binding exact diagonalization technique. They allow us to obtain numerically the local density of states as a function of energy and position, as well as an analytical form of the Friedel oscillations in the…
The adhesion of graphene on slightly lattice-mismatched surfaces, for instance of hexagonal boron nitride (hBN) or Ir(111), gives rise to a complex landscape of sublattice symmetry-breaking potentials for the Dirac fermions. Whereas a gap at the Dirac point opens for perfectly lattice-matched graphene on hBN, we show that the small lattice incommensurability prevents the opening of this gap and rather leads to a renormalized Dirac dispersion with a trigonal warping. This warping breaks the effective time reversal symmetry in a single valley. On top of this a new set of massless Dirac fermions …
The band structure of ABC-stacked N-layer graphene comprises topologically corresponding flat surface and gapped bulk subbands, as a consequence of the unique stacking configuration. In this paper, the bulk subbands are for the first times ever obtained for arbitrary N. A non-perturbative effective Hamiltonian closed in the bulk subspace is derived and used. The gapped bulk subbands are shown to evolve towards the zero energy with increasing N and in the infinite limit, they touch linearly along a circle. This outcome is a manifestation of the dimensional crossover to a three-dimensional Dirac…
The electronic properties of one-dimensional graphene superlattices strongly depend on the atomic size and orientation of the 1D external periodic potential. Using a tight-binding approach, we show that the armchair and zigzag directions in these superlattices have a different impact on the renormalization of the anisotropic velocity of the charge carriers. For symmetric potential barriers, the velocity perpendicular to the barrier is modified for the armchair direction while remaining unchanged in the zigzag case. For asymmetric barriers, the initial symmetry between the forward and backward …
Based on first-principles method we predict a new low-energy Stone-Wales graphene SW40, which has an orthorhombic lattice with Pbam symmetry and 40 carbon atoms in its crystalline cell forming well-arranged Stone-Wales patterns. The calculated total energy of SW40 is just about 133 meV higher than that of graphene, indicating its excellent stability exceeds all the previously proposed graphene allotropes. We find that SW40 processes intrinsic Type-III Dirac-cone (Phys. Rev. Lett., 120, 237403, 2018) formed by band-crossing of a local linear-band and a local flat-band, which can result in highl…
Landau levels of AB-stacked four- to six-layer graphene were studied experimentally in the presence of a perpendicular electric field. The Landau levels at a low magnetic field showed a characteristic structure that originated from the mini-Dirac cones created by the perpendicular electric fields. Six-fold or twelve-fold degenerate Landau levels arising from the mini-Dirac cones were observed in the vicinity of the charge neutrality point as a radial structure in a plot of their Landau fan diagrams. The structure of four-layer graphene had approximate electron-hole symmetry near the charge neu…
This paper presents a theoretical analysis on bulk and edge states in honeycomb lattice photonic crystals with and without time-reversal and/or space-inversion symmetries. Multiple Dirac cones are found in the photonic band structure and the mass gaps are controllable via symmetry breaking. The zigzag and armchair edges of the photonic crystals can support novel edge states that reflect the symmetries of the photonic crystals. The dispersion relation and the field configuration of the edge states are analyzed in detail in comparison to electronic edge states. Leakage of the edge states to free…
By means of atomistic tight-binding calculations, we investigate the effects of uniaxial strain on the electronic bandstructure of twisted graphene bilayer. We find that the bandstructure is dramatically deformed and the degeneracy of the bands is broken by strain. As a conseqence, the number of Dirac cones can double and the van Hove singularity points are separated in energy. The dependence of these effects on the strength of strain, its applied direction and the twist angle is carefully clarified. As an important result, we demonstrate that the position of van Hove singularities can be modu…
Strong band engineering in two-dimensional (2D) materials can be achieved by introducing moiré superlattices, leading to the emergence of various novel quantum phases with promising potential for future applications. Presented works to create moiré patterns have been focused on a twist embedded inside channel materials or between channel and substrate. However, the effects of a twist inside the substrate materials on the unaligned channel materials are much less explored. In this work, we report the realization of superlattice multi-Dirac cones with the coexistence of the main Dirac cone in a …
We study the electronic transport through np and npn junctions for AAA-stacked trilayer graphene. Two kinds of gates are considered where the first is a single gate and the second is a double gate. After obtaining the solutions for the energy spectrum, we use the transfer matrix method to determine the three transmission probabilities for each individual cone $τ=0, \pm 1$. We show that the quasiparticles in AAA-stacked trilayer graphene are not only chiral but also labeled by an additional cone index $τ$. The obtained bands are composed of three Dirac cones that depend on the chirality indexes…
Flat bands, Dirac cones, and higher-order band crossings in twisted multilayer graphene
该研究针对两层n层Bernal堆叠石墨烯的手性极限，证明能带结构存在三分法规律，推翻了该类模型仅能有高阶能带交叉或平带的传统认知，发现了新型拓扑相变。
We demonstrate that AA-stacked bilayer graphene (AA-BLG) encapsulated by dielectric materials can possess an energy gap due to the induced mass term. Using the four-band continuum model, we evaluate transmission and reflection probabilities along with the respective conductance. Considering interlayer mass-term difference opens a gap in the energy spectrum and also couples the two Dirac cones. This cone coupling induces an inter-cone transport that is asymmetric with respect to the normal incidence in the presence of asymmetric mass-term. The energy spectrum of the gapped AA-BLG exhibits elect…
Mirror-symmetric magic-angle twisted trilayer graphene (MATTG) hosts flat electronic bands close to zero energy, and has been recently shown to exhibit abundant correlated quantum phases with flexible electrical tunability. However studying these phases proved challenging as these are obscured by intertwined Dirac bands. In this work, we demonstrate a novel spectroscopy technique, that allows to quantify the energy gaps and Chern numbers of the correlated states in MATTG by driving band crossings between Dirac cone Landau levels and the energy gaps in the flat bands. We uncover hard correlated…
Graphene thermionic electron emission across high-interface-barrier involves energetic electrons residing far away from the Dirac point where the Dirac cone approximation of the band structure breaks down. Here we construct a full-band model beyond the simple Dirac cone approximation for the thermionic injection of high-energy electrons in graphene. We show that the thermionic emission model based on the Dirac cone approximation is valid only in the graphene/semiconductor Schottky interface operating near room temperature, but breaks down in the cases involving high-energy electrons, such as g…
We study the charge carriers transport in an AA-stacked bilayer graphene modulated by a lateral one-dimensional multibarrier structure. We investigate the band structures of our system, that is made up of two shifted Dirac cones, for finite and zero gap. We use the boundary conditions to explicitly determine the transmission probability of each individual cone ($τ=\pm 1$) for single, double and finite periodic barrier structure. We find that the Klein tunneling is only possible when the band structure is gapless and can occur at normal incidence as a result of the Dirac nature of the quasipart…
Graphene/h-BN has emerged as a model van der Waals heterostructure, and the band structure engineering by the superlattice potential has led to various novel quantum phenomena including the self-similar Hofstadter butterfly states. Although newly generated second generation Dirac cones (SDCs) are believed to be crucial for understanding such intriguing phenomena, so far fundamental knowledge of SDCs in such heterostructure, e.g. locations and dispersion of SDCs, the effect of inversion symmetry breaking on the gap opening, still remains highly debated due to the lack of direct experimental res…
Artificial lattices provide a tunable platform to realize exotic quantum devices. A well-known example is artificial graphene (AG), in which electrons are confined in honeycomb lattices and behave as massless Dirac fermions. Recently, AG systems have been constructed by manipulating molecules using scanning tunnelling microscope tips, but the nanoscale size typical for these constructed systems are impossible for practical device applications and insufficient for direct investigation of the electronic structures using angle-resolved photoemission spectroscopy (ARPES). Here, we demonstrate the …
We study structural and electronic properties of graphene grown on SiC substrate using scanning tunneling microscope (STM), spot-profile-analysis low energy electron diffraction (SPA-LEED) and angle resolved photoemission spectroscopy (ARPES). We find several new replicas of Dirac cones in the Brillouin zone (BZ). Their locations can be understood in terms of combination of basis vectors linked to SiC 6x6 and graphene 6xsqrt(3) x 6sqrt(3) reconstruction. Therefore these new features originate from the Moie caused by the lattice mismatch between SiC and graphene. More specifically, Dirac cones …
Ultimate In-plane Magnetoresistance Ratio of Graphene by Controlling the Gapped Dirac Cone through Pseudospin
本文通过赝自旋控制Ni(111)夹持石墨烯的狄拉克锥带隙，实现高达1450%的磁阻，并预测纳米尺度宽度可达到极限磁阻。
Kondo effect in twisted bilayer graphene
本文基于Bistritzer-MacDonald模型与数值重整化群方法，研究魔角扭曲双层石墨烯中磁性杂质的近藤效应，揭示零温与实验有限温度下的不同屏蔽行为。
It is highly desirable to integrate graphene into existing semiconductor technology, where the combined system is thermodynamically stable yet maintain a Dirac cone at the Fermi level. Firstprinciples calculations reveal that a certain transition metal (TM) intercalated graphene/SiC(0001), such as the strongly-bound graphene/intercalated-Mn/SiC, could be such a system. Different from free-standing graphene, the hybridization between graphene and Mn/SiC leads to the formation of a dispersive Dirac cone of primarily TM d characters. The corresponding Dirac spectrum is still isotropic, and the tr…
In this paper we systemically study the optical conductivity and density of states of disorded graphene beyond the Dirac cone approximation. The optical conductivity of graphene is computed by using the Kubo formula, within the framework of a full π-band tight-binding model. Different types of non-correlated and correlated disorders are considered, such as random or Gaussian potentials, random or Gaussian nearest-neighbor hopping parameters, randomly distributed vacancies or their clusters, and random adsorbed hydrogen atoms or their clusters. For a large enough concentration of resonant impur…
Chiral symmetry, fundamental in the physics of graphene, guarantees the existence of topologically stable doubled Dirac cones and anomalous behaviors of the zero-energy Landau level in magnetic fields. The crucial role is inherited in the optical responses and many-body physics in graphene, which are explained in this paper. We also give an overview of multilayer graphene from the viewpoint of the optical properties and their relation with the chiral symmetry.
In this paper we study the excitation spectrum of graphene in a strong magnetic field, beyond the Dirac cone approximation. The dynamical polarizability is obtained using a full $π$-band tight-binding model where the effect of the magnetic field is accounted for by means of the Peierls substitution. The effect of electron-electron interaction is considered within the random phase approximation, from which we obtain the dressed polarization function and the dielectric function. The range of validity of the Landau level quantization within the continuum approximation is studied, as well as the n…
Mapping borophene onto graphene: Quasi-exact solutions for guiding potentials in tilted Dirac cones
本文提出一种变换方法，将石墨烯一维势的狄拉克方程解映射到硼烯等倾斜狄拉克材料中，并证明平滑电子波导可调控谷极化，为谷电子学器件设计提供理论工具。
We study the electronic properties of a twisted trilayer graphene, where two of the layers have Bernal stacking and the third one has a relative rotation with respect to the AB-stacked layers. Near the Dirac point, the AB-twisted trilayer graphene spectrum shows two parabolic Bernal-like bands and a twisted-like Dirac cone. For small twist angles, the parabolic bands present a gap that increases for decreasing rotation angle. There is also a shift in the twisted-like Dirac cone with a similar angle dependence. We correlate the gap in the trilayer with the shift of the Dirac cone in an isolated…
We uncover a new type of magic-angle phenomena when an AA-stacked graphene bilayer is twisted relative to another graphene system with band touching. In the simplest case this constitutes a trilayer system formed by an AA-stacked bilayer twisted relative to a single layer of graphene. We find multiple anisotropic Dirac cones coexisting in such twisted multilayer structures at certain angles, which we call "Dirac magic." We trace the origin of Dirac magic angles to the geometric structure of the twisted AA-bilayer Dirac cones relative to the other band-touching spectrum in the moiré reciprocal …
We discuss plasmons of biased twisted bilayer graphene when the Fermi level lies inside the gap. The collective excitations are a network of chiral edge plasmons (CEP) entirely composed of excitations in the topological electronic edge states (EES) that appear at the AB-BA interfaces. The CEP form an hexagonal network with an unique energy scale $ε_p=\frac{e^2}{ε_0εt_0}$ with $t_0$ the moiré lattice constant and $ε$ the dielectric constant. From the dielectric matrix we obtain the plasmon spectra that has two main characteristics: (i) a diverging density of states at zero energy, and (ii) the …
The important experimental advances in graphene fabrication and its peculiar transport properties motivated researchers to utilize graphene as a potential basis for the next generation of fast and smart electronic devices. In this article, we investigate the influence of a potential substrate on the transport properties of a biased AA-stacked n-p-n bilayer graphene junction (AA-BLG). Using the Dirac Hamiltonian with the transfer matrix approach we obtain the transmission probabilities and thus the respective conductance. In the presence of the induced mass-term, the energy spectrum and the int…
Finite-frequency anomaly-induced electromechanical response of Dirac fermions in deformed graphene
研究了变形石墨烯中Dirac费米子在有限频率下的异常诱导电磁机械响应，通过几何电子-声子顶点建立了机械与电子的直接联系，并探讨了不同变形模式下产生的横向电流和电荷调制机制。
The extraordinary electronic properties of Dirac materials, the two-dimensional partners of Weyl semimetals, arise from the linear crossings in their band structure. When the dispersion around the Dirac points is tilted, the emergence of intricate transport phenomena has been predicted, such as modified Klein tunnelling, intrinsic anomalous Hall effects and ferrimagnetism. However, Dirac materials are rare, particularly with tilted Dirac cones. Recently, artificial materials whose building blocks present orbital degrees of freedom have appeared as promising candidates for the engineering of ex…
This thesis studies how the rudimentary attributes of graphene's charge carriers, and local moments on its surface, can be directly manipulated and controlled with electrostatic potentials. We first consider bilayer graphene subject to a spatially varying electrostatic potential that forms two neighbouring regions with opposite interlayer bias. Along the boundary, 1D chiral "kink" states emerge. We find that these 1D modes behave as a strongly interacting Luttinger liquid whose properties can be tuned via an external gate. Next, we consider superlattices in bilayer graphene. Superlattices are …
Angle-resolved photoemission and X-ray diffraction experiments show that multilayer epitaxial graphene grown on the SiC(000-1) surface is a new form of carbon that is composed of effectively isolated graphene sheets. The unique rotational stacking of these films cause adjacent graphene layers to electronically decouple leading to a set of nearly independent linearly dispersing bands (Dirac cones) at the graphene K-point. Each cone corresponds to an individual macro-scale graphene sheet in a multilayer stack where AB-stacked sheets can be considered as low density faults.
We compute the optical conductivity of graphene beyond the usual Dirac cone approximation, giving results that are valid in the visible region of the conductivity spectrum. The effect of next nearest neighbor hoping is also discussed. Using the full expression for the optical conductivity, the transmission and reflection coefficients are given. We find that even in the optical regime the corrections to the Dirac cone approximation are surprisingly small (a few percent). Our results help in the interpretation of the experimental results reported by Nair {\it et al.} [Science {\bf 320}, 1308 (20…
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