Excitonic instability in two-dimensional degenerate semimetals

We study the possibility of excitonic pairing in layered degenerate semimetals such as graphite, where the electron density of states almost vanishes at the Fermi level and, therefore, the Coulomb interactions remain essentially unscreened. By focusing on the Dirac-like low-energy electron excitations and numerically solving a non-linear gap equation for the order parameter, we obtain a critical value of the Coulomb coupling and establish the Kosterlitz-Thouless-like nature of a putative semimetal-to-excitonic insulator transition.