Optical conductivity as a probe of the interaction-driven metal in rhombohedral trilayer graphene

Rhombohedral trilayer graphene (RTG) has been the focus of special interest in the last years, since it hosts a variety of interaction-driven phases, with the metallic ones yielding exotic superconducting orders upon doping [H. Zhou et al, Nature 598, 429 (2021); ibid. 598, 434 (2021)]. In this work we compute the optical conductivity (using the low-energy effective theory ) for the three proposed paramagnetic metallic ground states: a fully gapped valence-bond state, the bond-current state and the rotational symmetry breaking charge-density wave. We show that the optical conductivity presents specific features for each of the aforementioned states and can therefore be used to distinguish between these different paramagnetic metallic ground states.