Berry curvature effects on quasiparticle dynamics in superconductors

TL;DR

This paper develops a semiclassical theory for superconducting quasiparticles that incorporates Berry curvature effects, revealing their impact on spectroscopic and transport properties, exemplified by twisted bilayer graphene.

Contribution

It introduces a novel framework linking Berry curvature to superconducting quasiparticle dynamics, highlighting effects from pairing geometry, supercurrent, and charge dipoles.

Findings

Berry curvature influences local density of states

Berry curvature affects thermal Hall conductivity

Application to twisted bilayer graphene shows induced effects

Abstract

We construct a theory for the semiclassical dynamics of superconducting quasiparticles by following their wave-packet motion and reveal rich contents of Berry curvature effects in the phase-space spanned by position and momentum. These Berry curvatures are traced back to the characteristics of superconductivity, including the nontrivial momentum-space geometry of superconducting pairing, the real-space supercurrent, and the charge dipole of quasiparticles. The Berry-curvature effects strongly influence the spectroscopic and transport properties of superconductors, such as the local density of states and the thermal Hall conductivity. As a model illustration, we apply the theory to study the twisted bilayer graphene with a $d_{x^{2}+y^{2}}+id_{xy}$ superconducting gap function, and demonstrate Berry-curvature induced effects.