Superconducting and excitonic quantum phase transitions in doped Dirac electronic systems

We investigate the effect of superconducting and excitonic interactions, as well as their competition, on Dirac electrons on a bipartite planar lattice. It is shown that, at half-filling, Cooper pairs and excitons coexist if the superconducting and excitonic coupling parameters are equal and above a threshold corresponding to a quantum critical point. In the case where only the excitonic interaction is present, we obtain a critical chemical potential, as a function of the interaction strength. Conversely, if only the superconducting interaction is considered, we show that the superconducting gap displays a characteristic dome as charge carriers are doped into the system. We also show that, as the chemical potential increases, superconductivity tends to suppress the excitonic order parameter.