相关论文: Equality of the bulk and edge Hall conductances in…
In this note, we prove the equality of the quantum bulk and the edge Hall conductances in mobility edges and in presence of disorder. The bulk and edge perturbations can be either of electric or magnetic nature. The edge conductance is…
We study the charge transport of the noninteracting electron gas in a two-dimensional quantum Hall system with Anderson-type impurities at zero temperature. We prove that there exist localized states of the bulk order in the…
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 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…
We prove quantization of the Hall conductance for continuous ergodic Landau Hamiltonians under a condition on the decay of the Fermi projections. This condition and continuity of the integrated density of states are shown to imply…
We investigate the chiral edge states in the two-dimensional ferromagntic kagom\'{e} lattice with spin anisotropies included. The system is periodic in the $x$ direction but has two edges in the $y$ direction. The Harper equation for…
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…
Two dimensional electron systems exhibiting the fractional quantum Hall effects are characterized by a quantized Hall conductance and a dissipationless bulk. The transport in these systems occurs only at the edges where gapless excitations…
An effective Chern-Simons theory for the Abelian quantum Hall states with edges is proposed to study the edge and bulk properties in a unified fashion. We impose a condition that the currents do not flow outside the sample. With this…
We would like to point out that: (i) according to the edge-bulk transport models for the quantum Hall regime, the direction of low bulk conductance is actually perpendicular to that expected naively; and (ii) the values of experimental…
Low-energy transport in quantum Hall states is carried through edge modes, and is dictated by bulk topological invariants and possibly microscopic Boltzmann kinetics at the edge. Here we show how the presence or breaking of symmetries of…
By designing a multi-channel millimeter Hall measurement configuration, we realize the carrier-density (locally) controllable measurement on the transport property in 2H MoS$_{2}$. We observe a linearly increased Hall conductivity and…
In a recent paper by S. Moroz, C. Hoyos, and L. Radzihovsky [Phys. Rev. B 91, 195409 (2015)], it is claimed that the conductivity at low frequency $\omega$ and small wavevector $q$ along the edge of a quantum Hall (QH) system (that…
We theoretically investigate electrical transport in a quantum Hall system hosting bulk and edge current carrying states. Spatially varying magnetic and electric confinement creates pairs of current carrying lines that drift in the same or…
The presence of chiral modes on the edges of quantum Hall samples is essential to our understanding of the quantum Hall effect. In particular, these edge modes should support ballistic transport and therefore, in a single particle picture,…
Edge states in the integral quantum Hall effect on a lattice are reviewed from a topological point of view. For a system with edges which is realized inevitably in an experimental situation, the Hall conductance $\sigma_{xy}$ is given by a…
We provide a short proof of the quantisation of the Hall conductance for gapped interacting quantum lattice systems on the two-dimensional torus. This is not new and should be seen as an adaptation of the proof of [1], simplified by making…
We present a theory of composite fermion edge states and their transport properties in the fractional and integer quantum Hall regimes. We show that the effective electro-chemical potentials of composite fermions at the edges of a Hall bar…
We consider the behaviour of quantum Hall edges away from the Luttinger liquid fixed point that occurs in the low energy, large system limit. Using the close links between quantum Hall wavefunctions and conformal field theories we construct…
In this paper, we rigorously prove the bulk-edge correspondence for finite two-dimensional ergodic disordered systems. Specifically, we focus on the short-range Hamiltonians with ergodic disordered on-site potentials. We first introduce the…