Related papers: On quantum Hall effect, Kosterlitz-Thouless phase …
We construct a generalization of the quantum Hall effect, where particles move in four dimensional space under a SU(2) gauge field. This system has a macroscopic number of degenerate single particle states. At appropriate integer or…
Interplay between the topological surface states and bulk states gives rise to diverse exotic transport phenomena in topological materials. The recently proposed Weyl orbit in topological semimetals in the presence of magnetic field is a…
It is shown that an account of the Berry phase (a topological $\theta$-term) together with a dissipative term in the effective action $S[\phi]$ of the tunnel contacts induces a strong quantization of the tunnel current at low temperatures.…
The Quantum Hall Effect for free electrons in external periodic field is discussed without using the linear response approximation. We find that the Hall conductivity is related in a simple way to Floquet energies (associated to the…
We review our work of the past decade on one-loop quantum corrections to the mass M and central charge Z of solitons in supersymmetric field theories: the kink, the vortex, and the monopoles (focussing on the kink and the monopoles here).…
The anomalous Hall effect (AHE), conventionally associated with time-reversal symmetry breaking in ferromagnetic materials, has recently been observed in nonmagnetic topological materials, raising questions about its origin. We unravel the…
Physical properties of anisotropic compressible quantum Hall states and their implications to integer quantum Hall effect are studied based on a mean field theory on the von Neumann lattice. It is found that the Hall gas has unusual…
Experimental data for fractional quantum Hall systems can to a large extent be explained by assuming the existence of a modular symmetry group commuting with the renormalization group flow and hence mapping different phases of…
The localization properties of electron states in the quantum Hall regime are reviewed. The random Landau model, the random matrix model, the tight-binding Peierls model, and the network model of Chalker and Coddington are introduced.…
Hall effect measurements are important for elucidating the fundamental charge transport mechanisms and intrinsic mobility in organic semiconductors. However, Hall effect studies frequently reveal an unconventional behavior that cannot be…
By restricting the motion of high-mobility 2D electron gas to a network of channels with smooth confinement, we were able to trace, both classically and quantum-mechanically, the interplay of backscattering, and of the bending action of a…
It is argued that the massive non-Abelian gauge field theory without involving Higgs bosons may be well established on the basis of gauge-invariance principle because the dynamics of the field is gauge-invariant in the physical space…
This paper presents the theory of Bohr-Sommerfeld-Heisenberg quantization of a completely integrable Hamiltonian system in the context of geometric quantization. The theory is illustrated with several examples.
Hall conductivity for the intrinsic quantum Hall effect in homogeneous systems is given by the topological invariant composed of the Green function depending on momentum of quasiparticle. This expression reveals correspondence with the…
We study the quantum Hall effect in a monolayer graphene by using an approach based on thermodynamical properties. This can be done by considering a system of Dirac particles in an electromagnetic field and taking into account of the edges…
The quantum Hall conductivity in the presence of constant magnetic field may be represented as the topological TKNN invariant. Recently the generalization of this expression has been proposed for the non - uniform magnetic field. \rev{The…
When charge transport occurs under conditions like topological protection or ballistic motion, the conductance of low-dimensional systems often exhibits quantized values in units of $e^{2}/h$, where $e$ and $h$ are the elementary charge and…
We argue that all anomalous transport properties of coherent quantum quantum Hall bilayers can be understood in terms of a mean-field transport theory in which the condensate phase is nearly uniform across the sample, and the strength of…
At partial filling of a flat band, strong electronic interactions may favor gapped states harboring emergent topology with quantized Hall conductivity. Emergent topological states have been found in partially filled Landau levels and…
We show that certain three-dimensional multigap topological insulators can host quantized integrated shift photoconductivities due to bulk invariants that are defined under reality conditions imposed by additional symmetries. We recast the…