There are two types of edge states in graphene with/without magnetic field. One is a quantum Hall edge state, which is topologically protected against small perturbation. The other is a chiral zero mode that is localized near the boundary with/without magnetic field. The latter is also topological but is guaranteed to be zero energy by the chiral symmetry, which is also responsible for massless Dirac like dispersion. Conceptual roles of the edge states are stressed and reviewed from a view point of the bulk-edge correspondence and the topological order.
To answer this question, we discuss the properties of electronic viscosity in deformed graphene by introducing strain and velocity gradient as pseudo-magnetic and pseudo-electric fields, respectively, into the Dirac model. We found that viscosity decreases with applied strain, simultaneously leading to a rather significant increase of the Reynolds number and enabling a real possibility for manifestation of noticeable turbulent effects in strained graphene.
Graphene and topological insulators (TI) possess two-dimensional Dirac fermions with distinct physical properties. Integrating these two Dirac materials in a single device creates interesting opportunities for exploring new physics of interacting massless Dirac fermions. Here we report on a practical route to experimental fabrication of graphene-Sb2Te3 heterostructure. The graphene-TI heterostructures are prepared by using a dry transfer of chemical-vapor-deposition grown graphene film. ARPES measurements confirm the coexistence of topological surface states of Sb2Te3 and Dirac π bands of grap…
Dirac fermions in graphene and analogues: magnetic field and topological properties
这是一个简短的回顾二维狄拉克费米子在石墨烯和类似的系统，如氮化硼，准二维有机盐$α$ -（BEDT-TTF）$_2$ I $_3$、光晶格中有冷原子的人造石墨烯等，重点是磁场性质（回旋轨道的半经典量子化、朗道能级、量子霍尔效应、磁等离子体、磁声子共振、磁输运等）以及拓扑性质（Berry相位、缠绕数、带间效应、Dirac点的合并跃迁等）。
Dirac point resonances due to atoms and molecules adsorbed on graphene and transport gaps and conductance quantization in graphene nanoribbons with covalently bonded adsorbates
In contrast to recent description [Phys. Rev. Lett. 106 (2011)116803], we show that pseudo spin in graphene is not completely a real angular momentum. The pseudo spin only in the direction perpendicular to graphene sheet is real angular momentum, while the pseudo spin parallel to graphene plane is still not real angular momentum. Interestingly, it is also shown that the Newtonian-like force and pseudo spin torque of massive Dirac electrons in graphene under strain field mimic gravitomagnetic force and gravitomagnetic spin torque, respectively. This is due to the equivalence of pseudo spin and …
We study how low-energy charge carriers scatter off periodic and linear graphene grain boundaries oriented along the zigzag direction with a periodicity three times greater than that of pristine graphene. These defects map the two Dirac points into the same position, and thus allow for intervalley scattering to occur. Starting from graphene's first-neighbor tight-binding model we show how can we compute the boundary condition seen by graphene's massless Dirac fermions at such grain boundaries. We illustrate this procedure for the 3-periodic pentagon-only grain boundary, and then work out the l…
The low energy physics of both graphene and surface states of three-dimensional topological insulators is described by gapless Dirac fermions with linear dispersion. In this work, we predict the emergence of a "heavy" Dirac fermion in a graphene/topological insulator hetero-junction, where the linear term almost vanishes and the corresponding energy dispersion becomes highly non-linear. By combining {\it ab initio} calculations and an effective low-energy model, we show explicitly how strong hybridization between Dirac fermions in graphene and the surface states of topological insulators can r…
Starting from an engineered periodic optical structure formed by waveguide arrays comprised of two interleaved lattices, we simulate a deformed Dirac equation. We show that the system also simulate graphene nano ribbons under strain. This optical analogue allows us to study the phenomenon of Zitterbewegung for the modified Dirac equation. Our results show that the amplitude of Zitterbewegung oscillations changes as the deformation parameter is changed.
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…
Graphene's electronic structure can be fundamentally altered when a substrate- or adatom-induced Kekulé superlattice couples the valley and isospin degrees of freedom. Here, we show that the band structure of Kekulé-textured graphene can be re-engineered through layer stacking. We predict a family of Kekulé graphene bilayers that exhibit band structures with up to six valleys, and room-temperature Dirac quasiparticles whose masses can be tuned electrostatically. Fermi velocities half as large as in pristine graphene put this system in the strongly coupled regime, where correlated ground states…
New Dirac points appear when periodic potentials are applied to graphene, and there are many interesting effects near these new Dirac points. Here we investigate the $\textit{Zitterbewegung}$ effect of fermions described by a Gaussian wave packet in graphene superlattice near new Dirac points. The $\textit{Zitterbewegung}$ near different Dirac points has similar characteristics, while Fermions near new Dirac points have different group velocities in both $x$- and $y$-direction, which causes the different properties of the $\textit{Zitterbewegung}$ near new Dirac points. We also investigate the…
Theory predicts that graphene under uniaxial compressive strain in an armchair direction should undergo a topological phase transition from a semimetal into an insulator. Due to the change of the hopping integrals under compression, both Dirac points shift away from the corners of the Brillouin zone towards each other. For sufficiently large strain, the Dirac points merge and an energy gap appears. However, such a topological phase transition has not yet been observed in normal graphene (due to its large stiffness) neither in any other electronic system. We show numerically and analytically th…
The recent developments in the emerging field of plasmonics in graphene and other Dirac systems are reviewed and a comprehensive introduction to the standard models and techniques is given. In particular, we discuss intrinsic plasmon excitations of single and bilayer graphene via hydrodynamic equations and the random phase approximation, but also comment on double and multilayer structures. Additionally, we address Dirac systems in the retardation limit and also with large spin-orbit coupling including topological insulators. Finally, we summarize basic properties of the charge, current and ph…
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…
To construct Lagrangian based on plate theory and tight-binding model, deflection-field coupling to Dirac fermions in graphene can be investigated. As have been known, deflection-induced strain may cause an effect on the motion of the electron, like a pseudo gauge field. In the present work, we will investigate the effect of the Dirac field on the motion of the deflection-field in graphene derived from Lagrangian density. Due to the interaction of the deflection- and Dirac-fields, the current-induced surface-tension up to about N/m in graphene membrane is predicted. This result may lead to con…
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 …
The charge carrier density in graphene on a dielectric substrate such as SiO$_2$ displays inhomogeneities, the so-called charge puddles. Because of the linear dispersion relation in monolayer graphene, the puddles are predicted to grow near charge neutrality, a markedly distinct property from conventional two-dimensional electron gases. By performing scanning tunneling microscopy/spectroscopy on a mesoscopic graphene device, we directly observe the puddles' growth, both in spatial extent and in amplitude, as the Dirac point is approached. Self-consistent screening theory provides a unified des…
We calculate the spectrum of massive Dirac fermions in graphene in the presence of an inhomogeneous magnetic field modeled by a step function. We find an analytical universal relation between the bandwidths and the propagating velocities of the modes at the border of the magnetic region, showing how by tuning the mass term one can control the speed of these traveling edge states.
We present an overview of the theoretical understanding of Hofstadter butterflies in monolayer and bilayer graphene. After a brief introduction on the past work in conventional semiconductor systems, we discuss the novel electronic properties of monolayer and bilayer graphene that helped to detect experimentally the fractal nature of the energy spectrum. We have discussed the theoretical background on the Moiré pattern in graphene. This pattern was crucial in determining the butterfly structure. We have also touched upon the role of electron-electron interaction in the butterfly pattern in gra…
The Dirac point and linear band structure in Graphene bestow it with remarkable electronic and optical properties, a subject of intense ongoing research. Explanations of high electronic mobility in graphene, often invoke the masslessness of electrons based on the effective relativistic Dirac-equation behavior, which are inaccessible to most undergraduate students and are not intuitive for non-physics researchers unfamiliar with relativity. Here, we show how to use only basic concepts from semiconductor theory and the linear band structure of graphene to explain its unusual effective mass and m…
Graphene on hexagonal boron nitride (hBN) can exhibit a topological phase via mutual crystallographic alignment. Recent measurements of nonlocal resistance ($R_{nl}$) near the secondary Dirac point (SDP) in ballistic graphene/hBN superlattices have been interpreted as arising due to the quantum valley Hall state. We report hBN/graphene/hBN superlattices in which $R_{nl}$ at SDP is negligible, but below 60 K approaches the value of $h/2e^{2}$ in zero magnetic field at the primary Dirac point with a characteristic decay length of 2 $μ$m. Furthermore, nonlocal transport transmission probabilities…
We have realized a Dirac fermion reflector in graphene by controlling the ballistic carrier trajectory in a sawtooth-shaped npn junction. When the carrier density in the inner p-region is much larger than that in the outer n-regions, the first straight np interface works as a collimator and the collimated ballistic carriers can be totally reflected at the second zigzag pn interface. We observed clear resistance enhancement around the np+n regime, which is in good agreement with the numerical simulation. The tunable reflectance of ballistic carriers could be an elementary and important step for…
Quantum confinement of graphene Dirac-like electrons in artificially crafted nanometer structures is a long sought goal that would provide a strategy to selectively tune the electronic properties of graphene, including bandgap opening or quantization of energy levels However, creating confining structures with nanometer precision in shape, size and location, remains as an experimental challenge, both for top-down and bottom-up approaches. Moreover, Klein tunneling, offering an escape route to graphene electrons, limits the efficiency of electrostatic confinement. Here, a scanning tunneling mic…
