| Modern condensed matter physics owes much of its success to Fermi liquid theory. In recent times, however, the study of strongly correlated particle systems is opening up all-new territory in many-body physics. A peculiar class of such systems, that of nodal fermions, is characterized by the quasiparticle density of states vanishing at the point-like Fermi surface and long-range inter-particle interactions surviving unscreened. In the first part, I discuss fermion pairing in one such system, 2D graphene. By solving the gap equation for the excitonic order parameter, I obtain values of critical interaction strength for a variety of power-law interactions and densities of states. Furthermore, these results are then used to compute the respective free energies and analyze possible phase transitions. In the second part, I discuss the effects of lattice disorder and impurities on the density of states in nodal fermion systems. These results and predictions will be of interest to a broad range of physical problems involving nodal fermions, and can be tested in a variety of experimental directions. |
