Related papers: Theory of integer quantum Hall effect in graphene
Recent experimental work on locally gated graphene layers resulting in p-n junctions have revealed quantum Hall effect in their transport behavior. We explain the observed conductance quantization which is fractional in the bipolar regime…
Recent successes in manufacturing of atomically thin graphite samples (graphene) have stimulated intense experimental and theoretical activity. The key feature of graphene is the massless Dirac type of low-energy electron excitations. This…
In two-dimensional (2D) electron systems under strong magnetic fields, interactions can cause fractional quantum Hall (FQH) effects. Bringing two 2D conductors to proximity, a new set of correlated states can emerge due to interactions…
We obtain an analytical expression for the Hall conductivity in AAA-stacked trilayer graphene (TLG) within the linear response Kubo formalism. Interestingly, we find that the quantization of the Hall conductivity is severely dependent on…
Topological quantum numbers account for the precise quantization that occurs in the integer Hall effect. In this theory, Kubo's formula for the conductance acquires a topological interpretation in terms of Chern numbers and their…
We numerically investigate the interplay of disorder and electron-electron interactions in the integer quantum Hall effect. In particular, we focus on the behaviour of the electronic compressibility as a function of magnetic field and…
A quantum statistical theory is developed for a fractional quantum Hall effects in terms of composite bosons (fermions) each of which contains a conduction electron and an odd (even) number of fluxons. The cause of the QHE is by assumption…
The quantum Hall effect in graphene p-n junctions is studied numerically with emphasis on the effect of disorder at the interface of two adjacent regions. Conductance plateaus are found to be attached to the intensity of the disorder, and…
It is widely believed that integer quantum Hall systems do not have fractional excitations. Here we show the converse to be true for a class of systems where integer quantum Hall effect emerges spontaneously due to the interplay of…
Graphene's honeycomb lattice structure underlies much of the remarkable physics inherent in this material, most strikingly through the formation of two ``flavors'' of Dirac cones for each spin. In the quantum Hall regime, the resulting…
We review the theoretical basis and understanding of electronic interactions in graphene Landau levels, in the limit of strong correlations. This limit occurs when inter-Landau-level excitations may be omitted because they belong to a…
The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. Existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external…
The von Neumann lattice representation is a convenient representation for studying several intriguing physics of quantum Hall systems. In this formalism, electrons are mapped to lattice fermions. A topological invariant expression of the…
The phase diagram of integer quantum Hall effect is numerically determined in the tight-binding model, which can account for overall features of recently obtained experimental phase diagram. In particular, the quantum Hall plateaus are…
We report on a study of interaction effects on the polarization of a disordered two-dimensional electron system in a strong magnetic field. Treating the Coulomb interaction within the time-dependent Hartree-Fock approximation we find…
We suggest that physics underlying the recently observed removal of sublattice and spin degeneracies in graphene in a strong magnetic field describes a phase transition connected with the generation of an excitonic gap. The experimental…
The quantum Hall conductivity in the presence of constant magnetic field may be represented as the topological TKNN invariant. Recently the generalization of this expression has been proposed for the non - uniform magnetic field. \rev{The…
We study the integer and fractional quantum Hall effect on a honeycomb lattice at half-filling (graphene) in the presence of disorder and electron-electron interactions. We show that the interactions between the delocalized chiral edge…
Computer modelling of the integer quantum Hall effect based on self-consistent Hartee-Fock calculations has now reached an astonishing level of maturity. Spatially-resolved studies of the electron density at near macroscopic system sizes of…
We discuss the fact that quantum capacitance of graphene-based devices leads to variation of it's charge density under changes of external magnetic field.The charge is conserved, but redistributes to substrate or other graphene sheet. We…