Interaction-driven instabilities of a Dirac semimetal

Abstract

We explore the possible particle-hole instabilities that can arise in a system of massless Dirac fermions on both the honeycomb and pi-flux square lattices with short range interactions. Through analytical and numerical studies we show that these instabilities can result in a number of interesting phases. In addition to the previously identified charge and spin density wave phases and the exotic `quantum anomalous Hall' (Haldane) phase, we establish the existence of the dimerized Kekule phase over a significant portion of the phase diagram and discuss the possibility of its spinful counterpart, the `spin Kekule' phase. On the pi-flux square lattice we also find various stripe phases, which do not occur on the honeycomb lattice. The Kekule phase is described by a Z3 order parameter whose singly quantized vortices carry fractional charge +/- e/2. On the pi-flux lattice the analogous dimerized phase is described by a Z4 order parameter. We perform a fully self-consistent calculation of the vortex structure inside the dimerized phase and find that close to the core the vortex resembles a familiar superconducting U(1) vortex, but at longer length scales a clear Z4 structure emerges with domain walls along the lattice diagonals.