Electronic Raman spectra in superconducting graphene: A probe of the pairing symmetry

Abstract

Motivated by the hot issue of the pairing symmetry of superconducting (SC) graphene, we theoretically study the electronic Raman spectra on a two-dimensional honeycomb lattice with two possible SC pairing symmetries, the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy}$ wave ($d+i{d}^{\ensuremath{'}}$ wave) and extended $s$ wave, at half filling and different doping levels. When it is not doped, the Raman spectrum for $d+i{d}^{\ensuremath{'}}$-wave pairing consists of a low-energy kink and a high-energy Raman peak, while the spectrum for the extended-$s$-wave pairing is similar to that in the normal state. On the other hand, when it is doped, besides the high-energy Raman peak, a low-energy pair breaking peak arises in both of the two pairings, which is forbidden in the otherwise normal state graphene at the same doping level. For the Raman spectrum of $d+i{d}^{\ensuremath{'}}$-wave pairing, there is an energy cutoff at low energy, below which no Raman absorption is allowed, indicating a full gap. While for the extended-$s$-wave pairing, with the increasing of the doping level, the low energy Raman behavior changes from a linear line to the appearance of cutoff energy, indicating that the gap changes from nodal to full. Therefore, we propose that the distinct features of Raman spectra can be used to differentiate the two pairings of SC graphene.