Pair density wave instability and Cooper pair insulators in gapped fermion systems

TL;DR

This paper investigates the emergence of pair density wave states in gapped fermion systems, revealing conditions for incommensurate and commensurate pairing, and highlighting the role of quantum fluctuations and strong correlations.

Contribution

It introduces a detailed analysis of pairing instabilities at finite momentum in band insulators, connecting incommensurate pairing to quantum fluctuations and strong-coupling phenomena.

Findings

Pair density wave instability occurs at finite momentum in band insulators.

Incommensurate pairing is highly sensitive to quantum fluctuations.

Strong coupling leads to commensurate pairing and exciton-like condensation.

Abstract

By analyzing simple models of fermions in lattice potentials we argue that the zero-temperature pairing instability of any ideal band-insulator occurs at a finite momentum. The resulting supersolid state is known as "pair density wave". The pairing momentum at the onset of instability is generally incommensurate as a result of phase-space restrictions and relative strengths of interband and intraband pairing. However, commensurate pairing occurs in the strong-coupling limit and becomes a Cooper-channel analogue of the Halperin-Rice exciton condensation instability in indirect bandgap semiconductors. The exceptional sensitivity of incommensurate pairing to quantum fluctuations can lead to a strongly-correlated insulating regime and a non-BCS transition, even in the case of weak coupling as shown by an exact renormalization group analysis.