Optical responses of Higgs and Leggett modes in multiband superconductors*

Collective excitations in superconductors are attracting much attention recently. One typical example is the Higgs mode, which is an amplitude mode of superconducting gap function. Higgs modes in superconductors are experimentally observed by Raman spectroscopy and optical measurements of third harmonic generation [1]. In multiband superconductors, the gap function contains multiple band degrees of freedom and becomes a matrix generally. Consequently, there appears another collective mode that corresponds to the oscillation of the relative phase between different bands, which is called Leggett modes. So far, Leggett modes are observed in Raman experiments using MgB2[2], while there is no optical measurement of Leggett modes.
Motivated by these, we study optical responses of Higgs and Leggett modes in multiband superconductors. We use a diagrammatic method to compute optical conductivities that arise from these collective excitations. We will discuss how these collective modes can be detected through (nonlinear) optical probes in the future experiments.
[1] R. Matsunaga et al., Science 345, 6201 (2014)
[2] G. Blumber et al., Physics Review Letters 99, 227002 (2007)