Pair density wave in the fractional quantum Hall effect at even denominator

TL;DR

This paper investigates the possibility of a pair density wave (PDW) state in the fractional quantum Hall effect at filling 5/2, proposing that a strong-pairing PDW may be a precursor to the nematic phase observed under pressure.

Contribution

It introduces a microscopic weak-coupling analysis suggesting that the relevant PDW state in the FQHE at 5/2 has a strong-pairing character, linking it to experimental phase transitions.

Findings

Proposes a strong-pairing PDW as a precursor to nematic phase.

Identifies a single collective mode associated with the order parameter.

Suggests weak-coupling regimes may favor PDW instability.

Abstract

The fractional quantum Hall effect (FQHE) at filling 5/2, which is usually understood as a $p$-wave paired state of underlying quasiparticles - composite fermions, transforms into a nematic phase under pressure \cite{csathy0, csathy}. A pair density wave (PDW) may be a precursor, underlying state for this behaviour, and such state(s) were proposed that maintain the weak-pairing feature of the uniform paired state \cite{frad}. Based on considerations in the weak-coupling regime of a microscopic description of the pairing phase (to mimic the phase as it gives way to a nematic phase in the experiments), we argue that the ensuing and relevant PDW state has a strong-pairing character. Furthermore, due to the existence of a single collective mode associated with the order parameter in the uniform paired phase, in the weak-coupling regime, the $p$-wave paired state, in general (for example, in the superconducting state of electrons), may be prone to a PDW instability.