Quantum Criticality of Semi-Dirac Fermions

Two-dimensional semi-Dirac fermions are quasiparticles that disperse linearly in one direction and quadratically in the other. We investigate instabilities of semi-Dirac fermions toward charge and spin density wave and superconducting orders, driven by short-range interactions. We analyze the critical behavior of the Yukawa theories for the different order parameters using Wilson momentum shell renormalization group. We generalize to a large number of fermion flavors, N, to achieve analytic control in 2+1 dimensions and calculate critical exponents at one-loop order, systematically including universal 1/N corrections. The anomalous dimension of the fermion fields vanishes in the large N limit, consistent with a recovery of Fermi-liquid behaviour. However, many other unusual features persist. We show that this is a consequence of non-analytic terms in the mean-field free energy of semi-Dirac fermions.