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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 review the basic aspects of electrons in graphene (two-dimensional graphite) exposed to a strong perpendicular magnetic field. One of its most salient features is the relativistic quantum Hall effect the observation of which has been the…
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…
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…
Monolayer graphene under a strong magnetic field near charge neutrality manifests the integer and fractional quantum Hall effects. Since only some of the four spin/valley flavors available to the electrons in each Landau level manifold are…
We have investigated the fractional quantum Hall states for the Dirac electrons in a graphene layer in different Landau levels. The relativistic nature of the energy dispersion relation of the electrons in the graphene significantly…
We numerically study the interplay of band structure, topological invariant and disorder effect in two-dimensional electron system of graphene in a magnetic field. Two \emph{distinct} quantum Hall effect (QHE) regimes exist in the energy…
We report on magneto-transport studies of dual-gated, Bernal-stacked trilayer graphene (TLG) encapsulated in boron nitride crystals. We observe a quantum Hall effect staircase which indicates a complete lifting of the twelve-fold degeneracy…
The quantum Hall effect in curved space has been the subject of many theoretical investigations in the past, but devising a physical system to observe this effect is hard. Many works have indicated that electronic excitations in strained…
We present an approach to the fractional quantum Hall effect observed in grapheme (GFQHE), basing us on the model developed previously for the fractional quantum Hall effect in a two-dimensional electron system embedded in a quantum well…
The observation of the anomalous quantum Hall effect in exfoliated graphene flakes triggered an explosion of interest in graphene. It was however not observed in high quality epitaxial graphene multilayers grown on silicon carbide…
Microwave transmission line spectroscopy is used to observe the integer quantum Hall effect in two samples of monolayer graphene with different geometries that are resistively-coupled to a coplanar waveguide. We find plateaus in transmitted…
In graphene, which is an atomic layer of crystalline carbon, two of the distinguishing properties of the material are the charge carriers two-dimensional and relativistic character. The first experimental evidence of the two-dimensional…
We review the effect of uniaxial strain on the low-energy electronic dispersion and Landau level structure of bilayer graphene. Based on the tight-binding approach, we derive a strain-induced term in the low-energy Hamiltonian and show how…
We discuss the quantum Hall effect of bilayer graphene with finite gate voltage where the Fermi energy exceeds the interlayer hopping energy. We calculated magnetic susceptibility, diagonal and off-diagonal conductivities in…
The effect of an inhomogeneous magnetic field which varies inversely as distance on the ground state energy level of graphene is studied. In this work, we analytically show that graphene under the influence of a magnetic field arising from…
The Hall resistance of a homogeneous electron system is well known to be anti-symmetric with respect to the magnetic field and the sign of charge carriers. We have observed that such symmetries no longer hold in planar hybrid structures…
We discuss the quantum Hall effect on a single-layer graphene in the framework of noncommutative (NC) phase space. We find it induces a shift in the Hall resistivity. Furthermore, comparison with experimental data reveals an upper bound on…
The quantum Hall effect (QHE) originates from discrete Landau levels forming in a two-dimensional (2D) electron system in a magnetic field. In three dimensions (3D), the QHE is forbidden because the third dimension spreads Landau levels…
The electromagnetic response of graphene in a magnetic field is studied, with particular emphasis on the quantum features of its ground state (vacuum). The graphene vacuum, unlike in conventional quantum Hall systems, is a dielectric medium…