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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…
We study theoretically the role of quenched magnetic disorder at the surface of a topological insulator by numerical simulation and scaling analysis. It is found that all the surface states are localized while the transverse conductivity is…
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…
The quantum Hall effect arises from the interplay between localized and extended states that form when electrons, confined to two dimensions, are subject to a perpendicular magnetic field. The effect involves exact quantization of all the…
The experimental progress in synthesizing low-dimensional nanostructures where carriers are confined to bent surfaces has boosted the interest in the theory of quantum mechanics on curved two-dimensional manifolds. It was recently asserted…
Quantized Hall conductance is a generic feature of two dimensional electronic systems with broken time reversal symmetry. In the quantum anomalous Hall state recently discovered in magnetic topological insulators, time reversal symmetry is…
The half-quantized anomalous Hall conductance (AHC) in topological materials is a condensed matter physics realization of the parity anomaly of (2+1) quantum field theory and an important challenge for both theoretical and experimental…
We review the construction of a low-energy effective field theory and its state space for "abelian" quantum Hall fluids. The scaling limit of the incompressible fluid is described by a Chern-Simons theory in 2+1 dimensions on a manifold…
The control of the electronic properties of materials via the vacuum fields of cavity electromagnetic resonators is one of the emerging frontiers of condensed matter physics. We show here that the enhancement of vacuum field fluctuations in…
The transport of a particle in the presence of a potential that changes periodically in space and in time can be characterized by the amount of work needed to shift a particle by a single spatial period of the potential. In general, this…
We present an effective medium theory that explains the disorder-induced transition into a phase of quantized conductance, discovered in computer simulations of HgTe quantum wells. It is the combination of a random potential and quadratic…
Topologically protected surface modes of classical waves hold the promise to enable a variety of applications ranging from robust transport of energy to reliable information processing networks. The integer quantum Hall effect has delivered…
Transport measurements on two dimensional electron systems in moderate magnetic fields suggest the existence of a spontaneously orientationally-ordered, compressible liquid state. We develop and analyze a microscopic theory of such a…
Topological states of quantum matter have inspired both fascinating physics findings and exciting opportunities for applications. Due to the over-complicated structure of, as well as interactions between, real materials, a faithful quantum…
Recently, Chern vector with arbitrary formula $\textbf{C}\!=\!(\mathcal{C}_{yz},\mathcal{C}_{xz},\mathcal{C}_{xy})$ in three-dimensional systems has been experimentally realized [\B{Nature 609, 925 (2022)}]. Motivated by these progresses,…
A two-dimensional (2D) topological insulator (TI) exhibits the quantum spin Hall (QSH) effect, in which topologically protected spin-polarized conducting channels exist at the sample edges. Experimental signatures of the QSH effect have…
In the quantum anomalous Hall effect, quantized Hall resistance and vanishing longitudinal resistivity are predicted to result from the presence of dissipationless, chiral edge states and an insulating 2D bulk, without requiring an external…
We present a composite fermion theory of tunneling into the edge of a compressible quantum Hall system. The tunneling conductance is non-ohmic, due to slow relaxation of electromagnetic and Chern-Simons field disturbances caused by the…
Fundamental topological phenomena in condensed matter physics are associated with a quantized electromagnetic response in units of fundamental constants. Recently, it has been predicted theoretically that the time-reversal invariant…
Quantum spin-Hall effect, a manifestation of topological properties that govern the behavior of surface states, was studied intensively in condensed matter physics resulting in the discovery of topological insulators. The quantum spin-Hall…