Quasi-particle propagation in quantum Hall systems

TL;DR

This paper investigates the geometrical and quantum statistical properties of particle propagation in quantum Hall systems, revealing discrete zeros, exclusion statistics, and edge correlation phenomena related to fractional statistics.

Contribution

It introduces new insights into the two-particle kernel zeros, short-distance exclusion effects, and impurity scattering impacts in quantum Hall geometries, advancing understanding of fractional statistics effects.

Findings

Discrete zeros in the two-particle kernel due to fractional statistics

Power-law behavior indicating exclusion statistics at short distances

Impurity scattering can suppress tunneling amplitudes at specific locations

Abstract

We study various geometrical aspects of the propagation of particles obeying fractional statistics in the physical setting of the quantum Hall system. We find a discrete set of zeros for the two-particle kernel in the lowest Landau level; these arise from a combination of a two-particle Aharonov-Bohm effect and the exchange phase related to fractional statistics. The kernel also shows short distance exclusion statistics, for instance, in a power law behavior as a function of initial and final positions of the particles. We employ the one-particle kernel to compute impurity-mediated tunneling amplitudes between different edges of a finite-sized quantum Hall system and and find that they vanishes for certain strengths and locations of the impurity scattering potentials. We show that even in the absence of scattering, the correlation functions between different edges exhibits unusual features for a narrow enough Hall bar.