# Interaction driven instabilities of a Dirac semi-metal

## TL;DR

This paper investigates particle-hole instabilities in Dirac semi-metals on honeycomb and pi-flux lattices, revealing new phases like the Kekule and stripe phases, with detailed vortex structure analysis.

## Contribution

It identifies and characterizes new dimerized Kekule and stripe phases in Dirac semi-metals, expanding understanding of their phase diagram with analytical and numerical methods.

## Key findings

- Discovery of the Kekule phase with Z3 order parameter
- Identification of stripe phases on pi-flux lattice
- Vortex structure analysis showing Z4 domain walls

## 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.