Related papers: Dirac fermions in a power-law-correlated random ve…
Graphene on a dielectric substrate exhibits spatial doping inhomogeneities, forming electron-hole puddles. Understanding and controlling the latter is of crucial importance for unraveling many of graphene's fundamental properties at the…
We consider systems described by the two-dimensional Dirac equation where the Fermi velocity is inhomogeneous as a consequence of mechanical deformations. We show that the mechanical deformations can lead to deflection and focusing of the…
We analyze by exact Renormalization Group (RG) methods the infrared properties of an effective model of graphene, in which two-dimensional massless Dirac fermions propagating with a velocity smaller than the speed of light interact with a…
Two-dimensional Dirac fermions are used to discuss quasiparticles in graphene in the presence of impurity scattering. Transport properties are completely dominated by diffusion. This may explain why recent experiments did not find weak…
We discuss the novel electronic properties of graphene under an external periodic scalar or vector potential, and the analytical and numerical methods used to investigate them. When graphene is subjected to a one-dimensional periodic scalar…
High-mobility graphene hosting massless charge carriers with linear dispersion provides a promising platform for electron optics phenomena. Inspired by the physics of dielectric optical micro-cavities where the photon emission…
Electron fractionalization is intimately related to topology. In one-dimensional systems, fractionally charged states exist at domain walls between degenerate vacua. In two-dimensional systems, fractionalization exists in quantum Hall…
We address the problem of Dirac fermions graphene quantum well and we focus on the low energy approximation for the Hamiltonian of the system where the former can be described by a Dirac-like Hamiltonian. Interesting relations are obtained…
In this paper, we study the massive Dirac equation with the presence of the Morse potential in polar coordinate. The Dirac Hamiltonian is written as two second-order differential equations in terms of two spinor wavefunctions. Since the…
Quasi-one-dimensional spin-Peierls and spin-ladder systems are characterized by a gap in the spin-excitation spectrum, which can be modeled at low energies by that of Dirac fermions with a mass. In the presence of disorder these systems can…
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…
We study the confinement of Dirac fermions in armchair graphene nanoribbons by means of a quantum-dot-type electrostatic potential. With the use of specific projection operators, we find exact solutions for some bound states that satisfy…
We study the confinement of Dirac fermions in graphene and in carbon nanotubes by an external magnetic field, mechanical deformations or inhomogeneities in the substrate. By applying variational principles to the square of the Dirac…
Random Dirac fermions in a two-dimensional space are studied numerically. We realize them on a square lattice using the $\pi$-flux model with random hopping. The system preserves two symmetries, the time-reversal symmetry and the symmetry…
Electronic properties of two-dimensional allotropes of carbon, such as graphene and its bilayer, multi-layer epitaxial graphene, few-layer Bernal-stacked graphene, as well as of three-dimensional bulk graphite are reviewed from the…
Experiments are finally revealing intricate facts about graphene which go beyond the ideal picture of relativistic Dirac fermions in pristine two dimensional (2D) space, two years after its first isolation. While observations of rippling…
The Dirac fermion in the random chiral models is studied which includes the random gauge field model and the random hopping model. We focus on a connection between continuum and lattice models to give a clear perspective for the random…
The density of states and differential entropy per particle are analyzed for Dirac-like electrons in graphene subjected to a perpendicular magnetic field and an in-plane electric field. For comparison, the derived density of states is…
The effects of a propagating sinusoidal out-of-plane flexural deformation in the electronic properties of a tense membrane of graphene are considered within a non-perturbative approach, leading to an electron-ripple coupling. The…
In the previous paper, we studied the random-mass Dirac fermion in one dimension by using the transfer-matrix methods and by introducing an imaginary vector potential in order to calculate the localization lengths. Especially we considered…