Excitonic instability in layered degenerate semimetals

We study excitonic pairing in quasi-two-dimensional degenerate semimetals such as graphite, where the electron density of states nearly vanishes at the Fermi level and, therefore, the Coulomb interactions remain unscreened. By focusing on the Dirac-like low-energy electronic excitations and numerically solving a non-linear gap equation for the excitonic order parameter, we obtain a critical value of the Coulomb coupling and establish the Kosterlitz-Thouless-like nature of the putative semimetal-to-excitonic insulator transition which can also be identified as a formal analog of chiral symmetry breaking in relativistic fermion theories