Pair density wave order from electron repulsion

TL;DR

This paper demonstrates the emergence of pair density wave order in models with repulsive electron interactions, revealing conditions for its stability and associated phase transitions, including a quantum critical point with non-Fermi liquid behavior.

Contribution

It introduces models that robustly produce PDW phases from repulsive interactions, elucidating the conditions necessary for their existence and characterizing their phase diagram.

Findings

PDW order requires non-monotonic and sufficiently strong repulsive couplings.

Phase diagram includes finite temperature PDW transitions.

Presence of a quantum critical point with non-Fermi liquid behavior.

Abstract

A pair density wave (PDW) is a superconductor whose order parameter is a periodic function of space, without an accompanying spatially-uniform component. Since PDWs are not the outcome of a weak-coupling instability of a Fermi liquid, a generic pairing mechanism for PDW order has remained elusive. We describe and solve models having robust PDW phases. To access the intermediate coupling limit, we invoke large $N$ limits of Fermi liquids with repulsive BCS interactions that admit saddle point solutions. We show that the requirements for long range PDW order are that the repulsive BCS couplings must be non-monotonic in space and that their strength must exceed a threshold value. We obtain a phase diagram with both finite temperature transitions to PDW order, and a $T=0$ quantum critical point, where non-Fermi liquid behavior occurs.