Related papers: Topological quantum numbers in the Hall effect
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 integral quantum Hall effect can be explained either as resulting from bulk or edge currents (or, as it occurs in real samples, as a combination of both). This leads to different definitions of Hall conductance, which agree under…
The entanglement entropy of the incompressible states of a realistic quantum Hall system are studied by direct diagonalization. The subdominant term to the area law, the topological entanglement entropy, which is believed to carry…
We found a quantum cohomology/homology of quantum Hall effect which arises as the invariant property of the Chern-Simons theory of quantum Hall effect and showed that it should be equivalent to the quantum cohomology which arose as the…
We prove a general theorem on the relation between the bulk topological quantum number and the edge states in two dimensional insulators. It is shown that whenever there is a topological order in bulk, characterized by a non-vanishing Chern…
It is shown, that a spectrum generating algebras and wave functions for the integral and fractional quantum Hall effect are related by the non-unitary similarity transformation. This transformation corresponds to the introduction of the…
Influences of topological defect and dislocation on conductivity behavior of charge carries in external electromagnetic fields are studied. Particularly the quantum Hall effect is investigated in detail. It is found that the nontrivial…
We derive the effective field theory from the microscopic Hamiltonian of interacting two-dimensional (pseudo) Dirac electrons by performing a statistic gauge transformation. The quantized Hall conductance are expected to be…
We establish the general phonon dynamics of magnetic solids by incorporating the Mead-Truhlar correction in the Born-Oppenheimer approximation. The effective magnetic-field acting on the phonons naturally emerges, giving rise to the phonon…
Recent work has extended topological band theory to open, non-Hermitian Hamiltonians, yet little is understood about how non-Hermiticity alters the topological quantization of associated observables. We address this problem by studying the…
We present a general formula for the topological part of the effective action for quantum Hall systems in higher dimensions, including fluctuations of the gauge field and metric around background fields of a specified topological class. The…
The Chern numbers which correspond to quantized Hall conductance $\sigma_{xy}$ were calculated for single- and bi-layer honeycomb lattices. The quantization of $\sigma_{xy}$ occurs in entire energy range. Several large jumps of Chern…
In a heterostructure of graphene and the ferromagnetic insulator EuO, the Eu atoms induce proximity exchange and inter-valley interactions in the graphene layer. Constrained by the lattice symmetries, and guided by ab initio calculations, a…
We study point-contact tunneling in the integer quantum Hall state of bosons. This symmetry-protected topological state has electrical Hall conductivity equal to $2 e^2/h$ and vanishing thermal Hall conductivity. In contrast to the integer…
The edge Hall conductivity is shown to be an integer multiple of $e^2/h$ which is almost surely independent of the choice of the disordered configuration. Its equality to the bulk Hall conductivity given by the Kubo-Chern formula follows…
The fractional quantum Hall effect (FQHE) of topological surface-state particles under a tilted strong magnetic field is theoretically studied by using the exact diagonalization method. The Haldane's pseudopotentials for the Coulomb…
We discuss a model of both classical and integer quantum Hall-effect which is based on a semi-classical Schroedinger-Chern-Simons-action, where the Ohm-equations result as equations of motion. The quantization of the classical…
We formulate the Kohn-Sham equations for the fractional quantum Hall effect by mapping the original electron problem into an auxiliary problem of composite fermions that experience a density dependent effective magnetic field.…
The status of the ac quantum Hall effect is reviewed with emphasis on the theoretical development in recent years. In particular, the numerical approaches for the calculation of the frequency dependent Hall and longitudinal conductivities…
Since the experimental realisation of the integer quantised Hall effect in a two dimensional electron system subject to strong perpendicular magnetic fields in 1980, a central question has been the interrelation between the conductance…