Instabilities Toward Charge Density Wave and Paired Quantum Hall State of Half-Filled Landau Levels

TL;DR

This paper investigates the stability of half-filled Landau levels, revealing conditions for charge density wave order and p-wave pairing, and discusses the competition between these states in relation to experimental observations.

Contribution

It introduces a model representing half-filled Landau levels with fermions and bosons coupled to gauge fields, identifying conditions for charge density wave and paired quantum Hall states.

Findings

Charge density wave order occurs under specific density conditions.

Enhanced gauge field fluctuations promote p-wave pairing.

The study connects theoretical predictions with recent experimental results.

Abstract

We study the stability of spin-resolved Landau levels at electron filling factor $\nu=n+1/2$, where n is a positive integer. Representing the half-filled topmost Landau level by fermions and the n filled inner Landau levels by n bosons, coupled to the Chern-Simons gauge fields, we show that the ground states exhibit charge density wave order for $n(n+1/2)>15.54 \pi(a_B^*)^2 n_e$, where $n_e$ is the 2D carrier density and $a_B^*$ is the effective Bohr radius. We find that the pairing interaction mediated by the fluctuating gauge field is enhanced near the charge density wave instability such that p-wave pairing of the Chern-Simons fermions prevails for $3.49(\pi{\ab}^2)n_e<n^2(n+1/2)<20.22\pi(a_B^*)^2 n_e$. The competition between charge density wave order and paired quantum Hall state is discussed in connection to recent experiments.