Linear spectroscopy of collective modes and the gap structure in two-dimensional superconductors

We consider optical response in multi-band, multi-layer two-dimensional superconductors. Within a simple model, we show that collective modes of the condensate, such as Leggett and clapping modes, can be detected in linear response. We show how trigonal warping of the superconducting order parameter can help facilitate detection of clapping modes. Taking rhombohedral trilayer graphene as an example, we consider several possible pairing mechanisms and show that all-electronic mechanisms may produce in-gap clapping modes. These modes, if present, should be detectable in the absorption of microwaves applied via gate electrodes; their detection would constitute strong evidence for unconventional pairing. Lastly, we show that absorption at frequencies above the superconducting gap 2|Δ| also contains a wealth of information about the gap structure. Our results suggest that linear spectroscopy can be a powerful tool for the characterization of unconventional two-dimensional superconductors.