Related papers: Noncommutative Graphene
The relevance of the strain-induced Dirac point shift to obtain the appropriate anisotropic Fermi velocity of strained graphene is demonstrated. Then a critical revision of the available effective Dirac Hamiltonians is made by studying in…
The proposals for realizing exotic particles through coupling of quantum Hall effect to superconductivity involve spatially non-uniform magnetic fields. As a step toward that goal, we study, both theoretically and experimentally, a system…
We consider the relationship between the tight-binding Hamiltonian of the two-dimensional honeycomb lattice of carbon atoms with nearest neighbor hopping only and the 2+1 dimensional Hamiltonian of quantum electrodynamics which follows in…
Similarity between the gravitoelectromagnetism and the electromagnetism is discussed. We show that the gravitomagnetic field (similar to the magnetic field) can be equivalent to the non-commutative effect of the momentum sector of the phase…
A connection is established between the continuum limit of the low-energy tight-binding description of graphene immersed in an in-plane magnetic field and the Chiral Magnetic Effect in Quantum Chromodynamics. A combination of mass gaps that…
We use supersymmetry transformations to obtain new one parameter family of inhomogeneous magnetic fields $\mathbf{B} = \widetilde{\mathcal{B}}(x,\lambda) \hat{e}_z$ for which the massless Dirac electron possesses exact solution. The…
We report on the properties of incompressible states of Dirac fermions in graphene in the presence of anisotropic interactions and a quantizing magnetic field. We introduce the necessary formalism to incorporate the anisotropy in 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…
The analytical expressions for both diagonal and off-diagonal ac and dc conductivities of graphene placed in an external magnetic field are derived. These conductivities exhibit rather unusual behavior as functions of frequency, chemical…
Graphene -a recently discovered one-atom-thick layer of graphite- constitutes a new model system in condensed matter physics, because it is the first material in which charge carriers behave as massless chiral relativistic particles. The…
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…
Two different points of view are available to understand the behavior of graphene at low energies. One is considering a large $N_F$ that makes graphene a semimetal, and another for small $N_F < 2.5$ that would make graphene a narrow gap…
We have discovered two-dimensional zero-gap material with a layered structure in the organic conductor $\alpha$-(BEDT-TTF)$_2$I$_3$ under high hydrostatic pressure. In contrast to graphene, the electron-hole symmetry is not good except at…
An analytical study of low-energy electronic excited states in an uniformly strained graphene is carried out up to second-order in the strain tensor. We report an new effective Dirac Hamiltonian with an anisotropic Fermi velocity tensor,…
The general covariance of the Dirac equation is exploited in order to explore the curvature effects appearing in the electronic properties of graphene. Two physical situations are then considered: the weak curvature regime, with…
In this document we explore graphene, a two-dimensional material with remarkable properties. We center our discussion around its electronic characteristics and their applications. We begin by giving a simple electronic model which will then…
This is a short review of two-dimensional Dirac fermions in graphene and similar systems such as boron nitride, quasi-2D organic salts $\alpha$-(BEDT-TTF)$_2$I$_3$, artificial graphene with cold atoms in optical lattices, etc. The emphasis…
We study graphene in an external magnetic field within a noncommutative (NC) framework. A gauge-invariant NC Hamiltonian is derived, and the system is analyzed using the ladder-operator formalism, yielding deformed Landau levels and…
Graphene research is currently one of the largest fields in condensed matter. Due to its unusual electronic spectrum with Dirac-like quasiparticles, and the fact that it is a unique example of a metallic membrane, graphene has properties…
Graphene is a two-dimensional carbon material with a honeycomb lattice and Dirac-type low-energy spectrum. In a strong magnetic field, where Coulomb interactions dominate against disorder broadening, quantum Hall ferromagnetic states…