Topological Mott Insulators

We consider extended Hubbard models with repulsive interactions on a honeycomb lattice, and the transitions from the semimetal to Mott insulating phases at half-filling. Because of the frustrated nature of the second-neighbor interactions, topological Mott phases displaying the quantum Hall and the quantum spin Hall effects are found for spinless and spin fermion models, respectively. The mean-field phase diagram is presented and the fluctuations are treated within the random phase approximation. Renormalization group analysis shows that these states can be favored over the topologically trivial Mott insulating states.

Figure 1

Interactions considered in our model Hamiltonian (leftmost plaquette), Eq. (1). Various order parameters are shown for the $A$ sublattice (open circles) and for the $B$ sublattice (filled circles) in the middle and right plaquettes. The QAH-QSH order parameters ${\chi }_A$, ${\chi }_B$ are complex 4-vectors associated with the directed second-neighbor links defined by ${\mathit{b}}_i$. In the case of spinless fermions, ${\chi }_A$ and ${\chi }_B$ are complex scalars.

Figure 2

Phase diagram for spinless fermions ($t=1$). The semimetallic (SM) state that occurs at weak coupling is separated from the CDW and the topological QAH states via a continuous transition. The line separating the QAH and CDW marks a first-order transition, which terminates at a bicritical point.

Figure 3

Complete mean-field phase diagram for the spinful model. The transitions from the semimetal (SM) to the insulating phases are continuous, whereas transitions between any two insulating phases are first order.

Figure 4

(a) Data for $U=0$, $V_1=1.4t$, $V_2=0$. Susceptibilities of each phase vs $T$ are shown: CDW (dash-dotted line); SDW (dotted line); QAH (solid line); and QSH (dashed line). (b) Same for $U=0$, $V_1=0$, $V_2=1.8t$ (QSH instability). The QSH phase has a larger susceptibility than QAH. Inset: fRG phase diagram at $U=0$, indicating SM and insulating regions (CDW dominates at large $V_1$, QSH at large $V_2$). The color bar corresponds to $T_c$ below which the insulating phases develop in fRG.