Emergent dome of nematic order around a quantum anomalous Hall critical point

Motivated by the experimental discovery of the quantum anomalous Hall effect and the interest in quantum phase transitions of correlated electrons, we consider interaction effects at a quantum anomalous Hall critical point. We study a microscopic lattice model of spinful fermions on the triangular lattice which exhibits a $C=2$ Chern insulator (CI) phase with a quantized anomalous Hall effect, sandwiched between two normal insulator (NI) phases. The first NI-CI quantum phase transition is driven by simultaneous mass inversion of a pair of Dirac fermions, with short range interactions being perturbatively irrelevant at the transition. The second CI-NI transition is driven by a quadratic band touching point protected by momentum space topology and $C_6$ lattice symmetry. A one-loop renormalization group analysis shows that short range interactions lead to a single marginally relevant perturbation at this transition. We obtain the mean field phase diagram of this model incorporating weak repulsive Hubbard interactions, finding an emergent dome of nematic order around this CI-NI topological critical point. We discuss the crossovers in the Hall conductivity at nonzero temperature, and the Landau theory of the quantum and thermal transitions out of the nematic phase. Our results may be relevant to ferromagnetic double perovskite films with spin-orbit coupling which have been proposed to host such a Chern transition. Our work provides perhaps the simplest example of an emergent phase near a quantum critical point.

Figure 1

Phase diagram for the noninteracting Hamiltonian as a function of $t_2$ and $\Delta$, at a fixed value of $t_3=t_1$. Here phases are CM (Chern metal), NM (normal metal), NI (normal insulator), and CI (Chern insulator). Nontrivial Chern numbers for the lower band are shown in parentheses.

Figure 2

Finite temperature mean field phase diagram showing the nematic dome (marked by solid red line) for the interacting Hamiltonian in Eq. (1) with $t_2/t_1=0.5$, $t_3/t_1=1$, and $U/t_1=8.5$. The $T=0$ phases are Chern insulator (CI), nematic Chern insulator (n-CI), nematic normal insulator (n-NI), and normal insulator (NI). The Chern transition, i.e., the nCI-nNI transition, is denoted by $★$. When nematic order is absent, the underlying quadratic band touching point occurs at $◯$. The dashed line (“Hall crossover”) marks the closing of the gap in the mean field spectrum; it signals a crossover in the anomalous Hall conductivity ${\sigma }_{xy}$ (shown in units of $e^2/h$).