Quantum Field Theory Description of Tunneling in the Integer Quantum Hall Effect

TL;DR

This paper develops a quantum field theory framework to analyze tunneling in the integer quantum Hall effect, predicting fractionalization phenomena and exact quantization of Hall conductivity, supported by numerical simulations.

Contribution

It introduces a field theory model linking microscopic parameters to tunneling behavior and predicts fractional charges and quantized Hall conductance at the interface.

Findings

Fermion number fractionalization can occur at the interface.

Exact quantization of Hall conductivity is demonstrated.

Numerical diagonalization supports the theoretical predictions.

Abstract

We study the tunneling between two quantum Hall systems, along a quasi one-dimensional interface. A detailed analysis relates microscopic parameters, characterizing the potential barrier, with the effective field theory model for the tunneling. It is shown that the phenomenon of fermion number fractionalization is expected to occur, either localized in conveniently modulated barriers or in the form of free excitations, once lattice effects are taken into account. This opens the experimental possibility of an observation of fractional charges with internal structure, close to the magnetic length scale. The coupling of the system to external gauge fields is performed, leading us to the exact quantization of the Hall conductivity at the interface. The field theory approach is well supported by a numerical diagonalization of the microscopic Hamiltonian.