Hall conductivity in the normal and superconducting phases of the Rashba system with Zeeman field

TL;DR

This paper investigates how intrinsic Hall conductivity varies between normal and superconducting phases in a Rashba system with Zeeman field, highlighting the impact of intra-band and inter-band pairing on topological properties.

Contribution

It reveals that inter-band pairing significantly affects Hall conductivity and provides insights into the topological nature of the superconducting phase in Rashba systems.

Findings

Inter-band pairing causes larger changes in Hall conductivity.

Hall conductivity change is linear in the pairing gap.

Inter-band pairing increases energy costs for topological phases.

Abstract

We study the intrinsic Hall conductivity of the ordinary and topological superconducting phases of a Rashba metal in a perpendicular Zeeman field. In this system the normal metal breaks time reversal symmetry while the superconducting order parameter does not, in contrast to the chiral p-wave superconducting state predicted in the monolayer strontium ruthenate (Sr$_2$RuO$_4$) whose Hall conductivity has been studied extensively. We study the effects of intra-band and inter-band pairing and find there is qualitatively larger change in the intrinsic Hall conductivity when there is inter-band pairing, with the change in magnitude linear in the pairing gap. We argue that inter-band pairing leads in general to higher energy costs for the topological phase compared to the topologically trivial phase and thus that the qualitative behavior of the intrinsic Hall conductivity with superconductivity in these systems could provide important clues about the nature of pairing in the superconducting phase and even some hints of whether it is topological or not.