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We study optical responses of Leggett modes in multiband superconductors inthe linear response regime. The Leggett mode is a collective mode unique tomultiband superconductors that arises from relative phase fluctuations ofsuperconducting orders for different bands. We use the Ginzburg-Landau (GL)description to study the collective modes in multiband systems. We find thatmultiband superconductors generally allow a linear coupling between the Leggettmode and external electric fields due to the presence of a cross term betweendifferent components of superconducting orders in the GL theory. The presenceof a linear coupling for the Leggett mode is in sharp contrast with the absenceof that for Higgs (amplitude) modes in single-band superconductors that onlysupport nonlinear optical responses such as third harmonic generation (THG). Wefurther confirm such a linear coupling in multiband superconductors by a moremicroscopic description based on a diagrammatic approach. We study thecollective modes within the random phase approximation (RPA) and compute theircontribution to the linear optical conductivity. These findings suggest a newroute to observe the Leggett mode by optical absorption.

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