Vertex correction for the linear and nonlinear optical responses in superconductors: multiband effect and topological superconductivity

TL;DR

This paper investigates how collective excitation modes, especially the Higgs mode, influence the linear and nonlinear optical responses in topological superconductors with multiband effects, revealing phenomena like sign reversal of photocurrent near topological transitions.

Contribution

It introduces a self-consistent response approximation to account for collective modes in optical responses of topological superconductors, highlighting the role of multiband effects and magnetic injection currents.

Findings

Higgs mode enhances optical responses near the Dirac point.

Sign reversal of photocurrent conductivity occurs around the topological transition.

Magnetic injection current is modified by the Higgs mode, enabling bulk detection of topological superconductivity.

Abstract

Intensive research has revealed intriguing optical responses in topological materials. This paper focuses on the optical responses in $s$-wave superconductors with a Rashba spin-orbit coupling and a magnetic field, one of the platforms of topological superconductivity. On the one hand, to satisfy some conservation laws in superconducting responses, it is essential to take into account collective excitation modes. On the other hand, the optical response is a promising phenomenon for detecting hidden collective modes in superconductors. In this paper, we investigate the effect of collective excitation modes on the linear and second-order optical responses based on the self-consistent response approximation, which is formulated using the Kadanoff-Baym method. Our main results reveal that the Higgs mode enhances the optical responses when the Fermi level is close to the Dirac point. The enhancement is due to the multiband effects characterized by interband pairing. We also demonstrate the sign reversal of the photocurrent conductivity around the topological transition with increasing the Zeeman field. This finding supports the prediction in our previous work without considering collective excitation modes [H. Tanaka, et al., Phys. Rev. B 110, 014520 (2024)]. The sign reversal phenomenon is attributed to the magnetic injection current modified by the Higgs mode, and is proposed for a bulk probe of topological superconductors. We also discuss the interplay of quantum geometry and collective modes.