Plasmon Modes and Correlation Functions in Quantum Wires and Hall Bars

TL;DR

This paper derives effective Hamiltonians for quantum wires and Hall bars, highlighting how their plasmon modes and correlation functions differ due to spatial electron separation in Hall systems.

Contribution

It provides microscopic derivations of low-energy boson Hamiltonians for quantum wires and Hall bars, emphasizing qualitative differences caused by electron separation.

Findings

Quantum Hall systems show suppressed quasi-solid correlations.

Plasmon dispersion relations differ between quantum wires and Hall bars.

Ground state correlation functions vary significantly due to electron separation.

Abstract

We present microscopic derivations of the one-dimensional low-energy boson effective Hamiltonians of quantum wire and quantum Hall bar systems. The quantum Hall system is distinguished by its spatial separation of oppositely directed electrons. We discuss qualitative differences in the plasmon collective mode dispersions and the ground state correlation functions of the two systems which are consequences of this difference. The slowly-decaying quasi-solid correlations expected in a quantum wire are strongly suppressed in quantum Hall bar systems.