Related papers: Electron fractionalization in two-dimensional grap…
The eigenstates of interacting electrons in the fractional quantum Hall phase typically form fairly well defined bands in the energy space. We show that the composite fermion theory gives insight into the origin of these bands and provides…
Chiral edge states of 2+1 dimensional Abelian and non-Abelian topological phases can be represented by chiral conformal field theories with integer and non-integer values of central charge, respectively. In this work we describe certain…
It is shown that three-dimensional systems of coupled quantum wires support fractional topological phases composed of closed loops and open planes of two-dimensional fractional quantum Hall subsystems. These phases have topologically…
Topological insulators have emerged as a major topic of condensed matter physics research with several novel applications proposed. Although there are now a number of established experimental examples of materials in this class, all of them…
The quantum Hall effect in graphene is regarded to be involving half-integer topological numbers associated with the massless Dirac particle, this is usually not apparent due to the doubling of the Dirac cones. Here we theoretically…
In this report we summarize a recent progress in exploration of correlated two-dimensional electron states in partially filled high Landau levels. At a mean-field Hartree-Fock level they can be described as charge-density waves, either…
A model system is considered where two dimensional electrons are confined by a harmonic potential in one direction, and are free in the other direction. Ground state in strong magnetic fields is investigated through numerical…
Defects play a key role in the electronic structure of graphene layers flat or curved. Topological defects in which an hexagon is replaced by an n-sided polygon generate long range interactions that make them different from vacancies or…
Fracton topological phases host fractionalized excitations that are either completely immobile or only mobile along certain lines or planes. We demonstrate how such phases can be understood in terms of two fundamentally different types of…
In this article we investigate the possibility of generating piezoelectric orbital polarization in graphene-like systems which are deformed periodically. We start with discrete two-level models which depend on control parameters; in this…
The formation of persistent charge currents in mesoscopic systems remains an interesting and actual topic of condensed matter research. Here, we analyze the formation of spontaneous arising persistent currents of charged fermions in…
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…
Topological semimetals are gapless states of matter which have robust surface states and interesting electromagnetic responses. In this paper, we consider the electromagnetic response of gapless phases in $3+1$-dimensions with line nodes.…
Physics of topological materials have attracted much attention from both physicists and mathematicians recently. The index and the fermion number of Dirac fermions play an important role in topological insulators and topological…
Motivated by the observation of the fractional quantum Hall effect in graphene, we consider the effective field theory of relativistic quantum Hall states. We find that, beside the Chern-Simons term, the effective action also contains a…
In a twisted graphene on hexagonal Boron Nitride, the presence of a gap and the breaking of the symmetry between carbon sublattices leads to multicomponent fractional quantum Hall effect (FQHE) due to the electrons correlation. We report on…
In this thesis, we consider fermion systems on square lattice spaces with a curved domain-wall mass term. In a similar way to the flat case, we find massless and chiral states localized at the wall. In the case of $S^1$ and $S^2$…
We consider a theory of a two-component Dirac fermion localized on a (2+1) dimensional brane coupled to a (3+1) dimensional bulk. Using the fermionic particle-vortex duality, we show that the theory has a strong-weak duality that maps the…
We present a general framework for analyzing fractionalized, time reversal invariant electronic insulators in two dimensions. The framework applies to all insulators whose quasiparticles have abelian braiding statistics. First, we construct…
Zero temperature states of matter are holographically described by a spacetime with an asymptotic electric flux. This flux can be sourced either by explicit charged matter fields in the bulk, by an extremal black hole horizon, or by a…