Related papers: Numerical study of quantum Hall effect in two-dime…
We study quantization conditions of the Hall conductivity for a two dimensional system described by a double exchange Hamiltonian with and without an external magnetic field. This is obtained by an extension of the topological arguments…
In QED of two space dimensions, a quantum Hall effect occurs in the absence of any magnetic field. We give a simple and transparent explanation. In solid state physics, the Hall conductivity for non-degenerate ground state is expected to be…
The past few years have produced major advances in our understanding of the quantum Hall effects---quantized and unquantized. Theories based on a mathematical transformation, where the electrons are replaced by a set of fermions interacting…
The surface states of topological insulators, which behave as charged massless Dirac fermions, are studied in the presence of a quantizing uniform magnetic field. Using the method of D.H. Lee[1], analytical formula satisfied by the energy…
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 purpose of these lectures is to describe the basic theoretical structures underlying the rich and beautiful physics of the quantum Hall effect. The focus is on the interplay between microscopic wavefunctions, long-distance effective…
Drawing on the connection with superconductivity, we give a simple AdS realization of the quantum Hall effect. The theory includes a statistical gauge field with a Chern-Simons term, in analogy with effective field theory models of the QHE.
Low-energy transport measurements in Quantum Hall systems have been argued to be governed by emergent modular symmetries whose predictions are robust against many of the detailed microscopic dynamics. We propose the recently-observed…
We investigate the intrinsic spin Hall effect in two-dimensional electron gases in quantum wells with two subbands, where a new intersubband-induced spin-orbit coupling is operative. The bulk spin Hall conductivity $\sigma^z_{xy}$ is…
Quantum Hall (QH) states are predicted to display an intriguing non-dissipative stress response to a shear deformation rate, a phenomenon variously known as asymmetric or Hall viscosity, or Lorentz shear response. Just as the QH effect…
We investigate the algebraic structure of flat energy bands a partial filling of which may give rise to a fractional quantum anomalous Hall effect (or a fractional Chern insulator) and a fractional quantum spin Hall effect. Both effects…
The quantum Hall effect in three-dimensional Weyl semimetal (WSM) receives significant attention for the emergence of the Fermi loop where the underlying two-dimensional Hall conductivity, namely, sheet Hall conductivity, shows quantized…
Hall effects are investigated for three-dimensional Dirac electrons as a model of bismuth alloys. It is found that there is unconventional contributions to the Hall conductivity $\sigma_{xy}$ generated by the interband effects of a magnetic…
We study the star lattice with Rashba spin-orbit coupling and exchange field and find that there exists the quantum anomalous Hall effect in this system and there are five energy gaps at Dirac points and quadratic band crossing points. We…
We predict the existence of a three dimensional quantum Hall effect plateau in a graphite crystal subject to a magnetic field. The plateau has a Hall conductivity quantized at $\frac{4e^2}{\hbar} \frac{1}{c_0} $ with $c_0$ the c-axis…
To fully appreciate the impacts that the discovery of the quantum Hall effect had on electrical metrology, it may benefit the reader to cultivate a general understanding of the phenomenon. Two-dimensional electron systems can exhibit many…
Research on graphene has revealed remarkable phenomena arising in the honeycomb lattice. However, the quantum spin Hall effect predicted at the K point could not be observed in graphene and other honeycomb structures of light elements due…
The recently synthesized silicene as well as theoretically discussed germanene are examples of buckled honeycomb structures. The buckled structures allow one to manipulate asymmetry between two underlying sublattices of honeycomb…
We introduce a supersymmetric Chern-Simons theory whose low energy physics is that of the fractional quantum Hall effect. The supersymmetry allows us to solve the theory analytically. We quantise the vortices and, by relating their dynamics…
Silicene is a monolayer of silicon atoms forming a two-dimensional honeycomb lattice, which shares almost every remarkable property with graphene. The low energy structure of silicene is described by Dirac electrons with relatively large…