Field Theory of Anisotropic Quantum Hall Gas: Metrology and a Novel Quantum Hall Regime

TL;DR

This paper uses the von Neumann lattice formalism to analyze anisotropic quantum Hall gases, deriving a topological invariant for Hall conductance, and discovers a new quantum Hall regime with unique transport properties.

Contribution

It introduces a topological invariant expression for Hall conductance within the von Neumann lattice formalism and reveals a novel quantum Hall regime with non-zero longitudinal resistance.

Findings

Derived a topological invariant expression for Hall conductance.

Identified a new quantum Hall regime with non-zero longitudinal resistance.

Analyzed thermodynamic and transport properties of anisotropic quantum Hall gas.

Abstract

The von Neumann lattice representation is a convenient representation for studying several intriguing physics of quantum Hall systems. In this formalism, electrons are mapped to lattice fermions. A topological invariant expression of the Hall conductance is derived and is used for the proof of the integer quantum Hall effect in the realistic situation. Anisotropic quantum Hall gas is investigated based on the Hartree-Fock approximation in the same formalism. Thermodynamic properties, transport properties, and unusual response under external modulations are found. Implications for the integer quantum Hall effect in the finite systems are also studied and a new quantum Hall regime with non-zero longitudinal resistance is shown to exist.