Related papers: The quantum Hall effect in graphene - a theoretica…
In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorist's perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of…
The quantum Hall effect is a remarkable manifestation of quantized transport in a two-dimensional electron gas. Given its technological relevance, it is important to understand its development in realistic nanoscale devices. In this work we…
We show that the manifestation of quantum interference in graphene is very different from that in conventional two-dimensional systems. Due to the chiral nature of charge carriers, it is sensitive not only to inelastic, phase-breaking…
When electrons are confined in two dimensions and subjected to strong magnetic fields, the Coulomb interactions between them become dominant and can lead to novel states of matter such as fractional quantum Hall liquids. In these liquids…
The unusual quantum Hall effect (QHE) in graphene is often discussed in terms of Dirac fermions moving with a linear dispersion relation. The same phenomenon will be explained in terms of the more traditional composite bosons, which move…
In two-dimensional (2D) electron systems in a magnetic field, the Coulomb interaction among charge carriers, under Landau quantization, essentially governs a variety of many-body phenomena while there are also phenomena, such as the…
Mechanical deformations of graphene induce a term in the Dirac Hamiltonian which is reminiscent of an electromagnetic vector potential. Strain gradients along particular lattice directions induce local pseudomagnetic fields and substantial…
We study the anomalous quantum Hall effect exhibited by the relativistic particles living on two-sphere S^2 and submitted to a magnetic monopole. We start by establishing a direct connection between the Dirac and Landau operators through…
Graphene enables precise carrier-density control via gating, making it an ideal platform for studying electronic interactions. However, sample inhomogeneities often limit access to the low-density regimes where these interactions dominate.…
Starting from the graphene lattice tight-binding Hamiltonian with an on-site U and long-range Coulomb repulsion, we derive an interacting continuum Dirac theory governing the low-energy behavior of graphene in an applied magnetic field.…
The effect of a varying pseudo-magnetic field, which falls as $1/x^2$, on a two dimensional electron gas in graphene is investigated. By considering the second order Dirac equation, we show that its correct general solution is that which…
This is a short non-technical introduction to applications of the Quantum Field Theory methods to graphene. We derive the Dirac model from the tight binding model and describe calculations of the polarization operator (conductivity). Later…
The Syst\`eme Internationale d'unit\'es (SI system) is about to undergo its biggest change in half a century by redefining the units for mass and current in terms of the fundamental constants h and e, respectively. This change crucially…
We report on the unusual nature of nu=0 state in the integer quantum Hall effect (QHE) in graphene and show that electron transport in this regime is dominated by counter-propagating edge states. Such states, intrinsic to massless Dirac…
We study the Euclidean effective action per unit area and the charge density for a Dirac field in a two--dimensional spatial region, in the presence of a uniform magnetic field perpendicular to the 2D--plane, at finite temperature and…
We investigate the emerging consequences of an applied strong in-plane electric field on a macroscopically large graphene sheet subjected to a perpendicular magnetic field, by determining in exact analytical form various many-body…
We numerically study the quantum Hall effect (QHE) in bilayer graphene based on tight-binding model in the presence of disorder. Two distinct QHE regimes are identified in the full energy band separated by a critical region with…
The quantum Hall effect (QHE) theoretically provides a universal standard of electrical resistance in terms of the Planck constant $h$ and the electron charge $e$. In graphene, the spacing between the lowest discrete energy levels occupied…
In this paper, we develop a unified theory for describing Hall effect in various electronic systems based on a pure electron picture (without the hole concept). We argue that the Hall effect is the magnetic field induced symmetry breaking…
Theoretical investigation of Dirac electrons in electrically modulated graphene under perpendicular magnetic field B is presented. We have carried out a detailed study of modulation effect on Dirac electrons, which determine its electrical…