Fate of the Superconducting Ground State on the Moyal Plane

TL;DR

This paper explores how noncommutative geometry, induced by Berry curvature, affects superconductivity, finding that noncommutativity weakens the pairing gap and makes superconducting states more fragile.

Contribution

It introduces a twisted quantum field theory approach to analyze superconductivity on the Moyal plane, revealing the impact of noncommutativity on pairing stability.

Findings

Noncommutativity reduces the superconducting gap.

Superconductivity becomes more fragile under noncommutative effects.

The analysis uses twisted quantum field theory techniques.

Abstract

It is known that Berry curvature of the band structure of certain crystals can lead to effective noncommutativity between spatial coordinates. Using the techniques of twisted quantum field theory, we investigate the question of the formation of a paired state of twisted fermions in such a system. We find that to leading order in the noncommutativity parameter, the gap between the non-interacting ground state and the paired state is {\it smaller} compared to its commutative counterpart. This suggests that BCS type superconductivity, if present in such systems, is more fragile and easier to disrupt.