Pair Density Waves from Local Band Geometry

TL;DR

This paper introduces a band-projection formalism to analyze superfluid weight in multi-orbital superconductors, revealing conditions under which a transition from BCS to pair-density wave states occurs due to local band geometry effects.

Contribution

It develops a formalism linking local band geometry to superfluid stiffness and demonstrates a geometric transition from BCS to PDW states in topological flat bands.

Findings

Band geometric superfluid stiffness can be locally non-positive-definite.

Non-positive-definite regions lead to a BCS-PDW transition.

Proof of the geometric BCS-PDW transition in topological flat bands.

Abstract

A band-projection formalism is developed for calculating the superfluid weight in two-dimensional multi-orbital superconductors with an orbital-dependent pairing. It is discovered that, in this case, the band geometric superfluid stiffness tensor can be locally non-positive-definite in some regions of the Brillouin zone. When these regions are large enough or include nodal singularities, the total superfluid weight becomes non-positive-definite due to pairing fluctuations, resulting in the transition of a BCS state to a pair-density wave (PDW). This geometric BCS-PDW transition is studied in the context of two-orbital superconductors, and proof of the existence of a geometric BCS-PDW transition in a generic topological flat band is established.