Optical response of the Leggett mode in multiband superconductors in the linear response regime

TL;DR

This paper investigates the optical response of Leggett modes in multiband superconductors, revealing a linear coupling to electric fields that enables potential optical detection, contrasting with single-band behaviors.

Contribution

It demonstrates, using Ginzburg-Landau and microscopic approaches, that Leggett modes in multiband superconductors have a linear optical coupling, unlike Higgs modes in single-band systems.

Findings

Leggett modes exhibit linear coupling to electric fields in multiband superconductors.

This coupling allows potential optical detection of Leggett modes.

Contrast with Higgs modes, which only show nonlinear optical responses.

Abstract

We study optical responses of Leggett modes in multiband superconductors in the linear response regime. The Leggett mode is a collective mode unique to multiband superconductors that arises from relative phase fluctuations of superconducting orders for different bands. We use the Ginzburg-Landau (GL) description to study the collective modes in multiband systems. We find that multiband superconductors generally allow a linear coupling between the Leggett mode and external electric fields due to the presence of a cross term between different components of superconducting orders in the GL theory. The presence of a linear coupling for the Leggett mode is in sharp contrast with the absence of that for Higgs (amplitude) modes in single-band superconductors that only support nonlinear optical responses such as third harmonic generation (THG). We further confirm such a linear coupling in multiband superconductors by a more microscopic description based on a diagrammatic approach. We study the collective modes within the random phase approximation (RPA) and compute their contribution to the linear optical conductivity. These findings suggest a new route to observe the Leggett mode by optical absorption.