Theory of light-induced resonances with collective Higgs and Leggett modes in multiband superconductors

TL;DR

This paper presents a theoretical study of how collective Higgs and Leggett modes in two-band superconductors can be resonantly excited by light, revealing their signatures in nonlinear optical responses and suggesting experimental detection methods.

Contribution

It introduces a mean-field framework showing resonant excitation of multiple collective modes in multiband superconductors via nonlinear light-matter interactions.

Findings

Higher-energy Higgs mode exhibits sharp resonance with light.

Lower-energy Higgs mode has a broadened resonance width.

Leggett mode can be resonantly excited by a homogeneous ac electric field.

Abstract

We theoretically investigate coherent optical excitations of collective modes in two-band BCS superconductors, which accommodate two Higgs modes and one Leggett mode corresponding, respectively, to the amplitude and relative-phase oscillations of the superconducting order parameters associated with the two bands. We find, based on a mean-field analysis, that each collective mode can be resonantly excited through a nonlinear light-matter coupling when the doubled frequency of the driving field coincides with the frequency of the corresponding mode. Among the two Higgs modes, the higher-energy one exhibits a sharp resonance with light, while the lower-energy mode has a broadened resonance width. The Leggett mode is found to be resonantly induced by a homogeneous ac electric field because the leading nonlinear effect generates a potential offset between the two bands that couples to the relative phase of the order parameters. The resonance for the Leggett mode becomes sharper with increasing temperature. All of these light-induced collective modes along with density fluctuations contribute to the third-harmonic generation. We also predict an experimental possibility of optical detection of the Leggett mode.