Related papers: The Canonical Flux Quantization and IQHE(revised)
We investigate the effect on a Quantum Hall (QH) liquid of its coupling to 3+1 dimensional dynamical electromagnetism, which renders the system gapless. We calculate both the Hall and longitudinal resistances, $\rho_H$ and $\rho_L$, in the…
Two-terminal conductance quantization in the context of quantum Hall (QH) physics is intimately related to the current carried by a discrete number of chiral edge modes. Upon pinching off a QH bar, one may engineer setups where some modes…
This article provides an accessible illustration of the measurement approach to the study of the quantum-classical transition suitable for beginning graduate students. As an example, we apply it to a quantum system with a general quadratic…
We demonstrate how integer quantization of Hall conductance arises from the large-scale geometry of the sample. Specifically, the Hall conductance is a higher-trace pairing of the Fermi projection with a coarse cohomology class coming from…
We present a two dimensional model of IQHE in accord with the cyclotron motion. The quantum equation of the QHE curve and a new definition of filling factor are also given.
Using canonical quantisation, and eschewing the Schwinger-Keldysh path integral, we derive a version of the Worldline Quantum Field Theory (WQFT) formalism suitable for both scattering and bound configurations of the classical two-body…
We study quantization conditions of the Hall conductivity for a two dimensional system described by a double exchange Hamiltonian with and without an external magnetic field. This is obtained by an extension of the topological arguments…
Using the fact that the nonintegrable phase factor can reformulate the gauge theory in terms of path dependent vector potentials, the quantization condition for the nonintegrable phase is investigated. It is shown that the path-dependent…
Understanding how classical physics emerges from quantum mechanics remains a central problem in the foundations of physics. Here we derive a classical limit from finite-resolution measurements, modeled by continuous coarse-grained POVMs.…
The hydrodynamical phase-slippage geometry and a semi-classical Josephson-RCSJ formulism are combined to make an analogy between the periodically driven Josephson ac effect and the quantum Hall effect. Both of these two macroscopic quantum…
The quantum valley Hall effect (QVHE) has been observed in a variety of experimental setups, both quantum and classical. While extremely promising for applications, one should be reminded that QVHE is not an exact topological phenomenon and…
We present an analytical scaling theory for localization in a two-dimensional hierarchical network model that is designed to represent phase-coherent electron transport in the quantum-Hall regime. Scaling expressions for both the…
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 quantization of resistances in the quantum Hall effect and ballistic transport through quantum point contacts is compared with the quantization of the charge relaxation resistance of a coherent mesoscopic capacitor. While the former two…
Using the fiber bundle concept developed in geometry and topology, the fractionally quantized Hall conductivity is discussed in the relevant many--particle configuration space. Electron-magnetic field and electron-electron interactions…
The equilibrium current distribution in a quantum Hall fluid that is subjected to a slowly varying confining potential is shown to generally consist of strips or channels of current, which alternate in direction, and which have universal…
We study the linear Hall response of 2D ballistic system on inhomogeneous magnetic field. We establish that in classical limit the Hall conductivity response on local magnetic field is quantized in units of $\alpha_H \equiv \frac{e^3}{2…
This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…
Incompressible Quantum Hall fluids (QHF's) can be described in the scaling limit by three-dimensional topological field theories. Thanks to the correspondence between three-dimensional topological field theories and two dimensional chiral…
The fate of integer quantum Hall effect (IQHE) at weak magnetic field is studied numerically in the presence of {\it correlated} disorders. We find a systematic {\it float-up} and {\it merging} picture for extended levels on the low-energy…