相关论文: Quantum Hall Effect and Noncommutative Geometry
We analyze the role of impurities in the fractional quantum Hall effect using a highly controllable system of ultracold atoms. We investigate the mechanism responsible for the formation of plateaux in the resistivity/conductivity as a…
We review quantum tunneling provoked by external field driving, focusing on the role of geometric effects. The discussion begins with an overview of tunneling phenomena, including the Landau-Zener model and the Schwinger effect, both of…
We clarify relations between the higher dimensional quantum Hall effect and A-class topological insulator. In particular, we elucidate physical implications of the higher dimensional non-commutative geometry in the context of A-class…
The $\nu=\frac{5}{2}$ fractional quantum Hall effect is of experimental and theoretical interest due to the possible non-Abelian statistics of the excitations in the electron liquid. A small voltage difference across a sample applied in…
We consider the quantum Hall effect in quantum electrodynamics and find a deviation from the quantum mechanical prediction for the Hall conductivity due to radiative antiscreening of electric charge in an external magnetic field. A weak…
The quantum geometry, comprising Berry curvature and quantum metric, plays a fundamental role in governing electron transport phenomena in solids. Recent studies show that the quantum metric dipole drives scattering-free nonlinear Hall…
We report on theoretical and experimental investigations of the integer quantized Hall effect in narrow channels at various mobilities. The Hall bars are defined electrostatically in two-dimensional electron systems by biasing metal gates…
We decompose the intrinsic second-order nonlinear Hall effect (NLHE) of a generic multiband system into its quantum-geometric contributions within a fully quantum-mechanical, projector-based formalism. By expanding the nonlinear…
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…
The boundary map in K-theory arising from the Wiener-Hopf extension of a crossed product algebra with R is the Connes-Thom isomorphism. In this article the Wiener Hopf extension is combined with the Heisenberg group algebra to provide an…
For a particle confined to the two-dimensional helical surface embedded in four-dimensional (4D) Euclidean space, the effective Hamiltonian is deduced in the thin-layer quantization formalism. We find that the gauge structure of the…
The quantum Hall regime in a smooth random potential is considered when two disorder-broadened Zeeman levels overlap strongly. Spin-orbit coupling is found to cause a drastic change in the percolation network which leads to a strong…
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…
We address the researchers studying the magneto-transport properties of unconventional systems such as bulk samples and new materials or those working in the soft quantum limit. We have developed a procedure for the analysis of experimental…
We theoretically study the finite-size effects in the dynamical response of a quantum anomalous Hall insulator in the disk geometry. Semi-analytic and numerical results are obtained for the wavefunctions and energies of the disk within a…
We numerically study the three-dimensional (3D) quantum Hall effect (QHE) and magnetothermoelectric transport of Weyl semimetals in the presence of disorder. We obtain a bulk picture that the exotic 3D QHE emerges in a finite range of Fermi…
The dynamical transport properties near the integer quantum Hall transition are investigated at zero temperature by means of the Dirac fermion approach. These properties have been studied experimentally at low frequency omega and low…
We describe the generic behavior of Fredholm indices in the space of Toeplitz operators. We relate this behavior to certain conjectures and open problems that arise in the context of the Quantum Hall Effect.
The quantum Hall effect under the influence of gravity and inertia is studied in a unified way. We make use of an algebraic approach, as opposed to an analytic approach. We examine how both the integer and the fractional quantum Hall…
We present an approach to the fractional quantum Hall effect observed in grapheme (GFQHE), basing us on the model developed previously for the fractional quantum Hall effect in a two-dimensional electron system embedded in a quantum well…