Related papers: Effective Edge State Dynamics in the Fractional Qu…
We note an implication of chiral Luttinger liquid based edge state description of the fractional quantum Hall effect. By considering several examples that involve backward moving neutral modes, arising from either composite fermions with…
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…
The Chern-Simons Ginzburg-Landau theory for the fractional Quantum Hall effect is studied in the presence of a confining potential. We review the bulk properties of the model and discuss how the plateau formation emerges without any…
This article reports on our microscopic investigations of the edge of the fractional quantum Hall state at filling factor $\nu=1/3$. We show that the interaction dependence of the wave function is well described in an approximation that…
Since the experimental realization of synthetic gauge fields for neutral atoms, the simulation of topologically non-trivial phases of matter with ultracold atoms has become a major focus of cold atom experiments. However, several obvious…
We present an analytic prescription for computing the edge dispersion E(k) of a tight-binding Dirac Hamiltonian terminated at an abrupt crystalline edge. Specifically, we consider translationally invariant Dirac Hamiltonians with…
The effects of impurity scattering on a general Abelian fractional quantum Hall (FQH) edge state are analyzed within the chiral-Luttinger-liquid model of low-energy edge dynamics. We find that some disordered edges can have several…
A general description of weak and strong tunneling fixed points is developed in the chiral-Luttinger-liquid model of quantum Hall edge states. Tunneling fixed points are a subset of `termination' fixed points, which describe boundary…
Quantum Hall Dynamics is formulated on von Neumann lattice representation where electrons in Landau levels are defined on lattice sites and are treated systematically like lattice fermions. We give a proof of the integer Hall effect, namely…
We show that there is an emergent lattice description for the continuous fractional quantum Hall (FQH) systems, with a generalised set of few-body coherent states. In particular, model Hamiltonians of the FQH effect are equivalent to the…
We report a theoretical study of the linear and nonlinear dynamics of edge excitations of an integer quantum Hall state of non-interacting fermions. New features beyond the chiral Luttinger liquid picture are anticipated to arise from the…
Fractional quantum Hall effect (FQHE) is a prime example of topological quantum many-body phenomena, arising from the interplay between strong electron correlation, topological order, and time reversal symmetry breaking. Recently, a lattice…
Elastic quantum bound-state reflection from a hard-wall boundary provides direct information regarding the structure and compressibility of quantum bound states. We discuss elastic quantum bound-state reflection and derive a general theory…
The magnetic field opens a gap in the edge state spectrum of two-dimensional topological insulators thereby destroying protection of these states against backscattering. To relate properties of this gap to parameters of the system and to…
Electrical currents in a quantum spin Hall insulator are confined to the boundary of the system. The charge carriers can be described as massless relativistic particles, whose spin and momentum are coupled to each other. While the helical…
The rapid development of artificial gauge fields in ultracold gases suggests that atomic realization of fractional quantum Hall physics will become experimentally practical in the near future. While it is known that bosons on lattices can…
We use the bulk Hamiltonian for a three-dimensional topological insulator such as $\rm Bi_2 Se_3$ to study the states which appear on its various surfaces and along the edge between two surfaces. We use both analytical methods based on the…
According to Wen's theory, a universal behavior of the fractional quantum Hall edge is expected at sufficiently low energies, where the dispersion of the elementary edge excitation is linear. A microscopic calculation shows that the actual…
The chiral Luttinger liquid theory for fractional quantum Hall edge transport predicts universal power-law behavior in the current-voltage ($I$-$V$) characteristics for electrons tunneling into the edge. However, it has not been…
Motivated by recent experimental advancements in scanning optical stroboscopic confocal microscopy and spectroscopy measurements, which have facilitated exceptional energy-space-time resolution for investigating edge and bulk dynamics in…