Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing

We investigate the stability of a quadratic band-crossing point (QBCP) in 2D fermionic systems. At the noninteracting level, we show that a QBCP exists and is topologically stable for a Berry flux $\pm 2\pi$ if the point symmetry group has either fourfold or sixfold rotational symmetries. This putative topologically stable free-fermion QBCP is marginally unstable to arbitrarily weak short-range repulsive interactions. We consider both spinless and spin-$1/2$ fermions. Four possible ordered states result: a quantum anomalous Hall phase, a quantum spin Hall phase, a nematic phase, and a nematic-spin-nematic phase.

Figure 1

(a) A checkerboard lattice and (b) a Kagome lattice. The arrows represent currents in a spontaneously generated QAH state that breaks the time-reversal symmetry. See text for details.

Figure 2

Mean-field $T\mathrm{\text{−}}V$ phase diagram of a half-filled checkerboard lattice with $t^{\prime }/t=0.5$, $t^{\prime \prime }/t=-0.2$. Nematic and QAH orders coexist in the shaded area. Thick (thin) lines are first (second) order transitions. $A$ is a bicritical point, and $B$ is a critical-end point.