Quantum hall transformer in a quantum point contact over the full range of transmission

TL;DR

This paper investigates the conductance behavior of a quantum Hall transformer in a quantum point contact, providing a microscopic understanding and full transmission range analysis using novel models and computational methods.

Contribution

It introduces a sliding charge density wave model to clarify the boundary sine Gordon description and computes conductance across all transmission levels.

Findings

Quantitative connection between BSG model and quantum Hall system

Conductance behavior explained over full transmission range

Validation through perturbative and matrix product state calculations

Abstract

A recent experiment [Cohen et al., Science 382, 542 (2023)] observed a robustly quantized $e^2/2h$ conductance in a quantum point contact between fractional quantum Hall edges (a quantum Hall transformer), which then vanishes at low temperature. While this behavior can be described by a boundary sine gordon (BSG) model derived from electron tunneling, the microscopic motivation for such strong tunneling is unclear. We use an alternative model based on sliding charge density waves and a density inhomogeneity to clarify the BSG description and calculate the conductance over the full range of transmission. Using a perturbative method and a matrix product state calculation, we draw a quantitative connection between the BSG model and the physical quantum Hall system.