Fluctuation-driven topological Hund insulators

We investigate the role of electron-electron interaction in a two-band Hubbard model based on the Bernevig-Hughes-Zhang Hamiltonian exhibiting the quantum spin Hall (QSH) effect. By means of dynamical mean-field theory, we find that a system with topologically trivial noninteracting parameters can be driven into a QSH phase at finite interaction strength by virtue of local dynamical fluctuations. For very strong interaction, the system reenters a trivial insulating phase by going through a Mott transition. We obtain the phase diagram of our model by direct calculation of the bulk topological invariant of the interacting system in terms of its single-particle Green's function.

Figure 1

Phase diagram of the BHZ model with $U$, $V=U-2J$, and $J=0.25U,\lambda =0.3$. For $m>2$ the noninteracting model is topologically trivial (green) and for $m<2$ is in a topologically nontrivial QSH phase (red). At large values of $U$ the system is in a Mott phase (blue). The red open circles at $m=0$ indicate that the solution is metallic. The gray lines denote transition regions. The “topological Hund insulator,” i.e., the nontrivial interacting phase in red, can be obtained for small-to-moderate values of $U$, starting from a trivial phase with $m\gtrsim 2$.

Figure 2

Orbital occupation as a function of the interaction strength for cases (i) $H_U+H_V+H_J$ (red), (ii) $H_U+H_V+H_J+H_S$ (blue), and (iii) $H_U$ (green). All plots show calculations performed at $k_{B}T=1/100$, $m=3$, and $\lambda =0.3$. The vertical dashed lines mark the topological transition, while the Mott transition takes place when $(n_H,n_E)=(1,1)$.

Figure 3

$\omega$ dependence of the real part of the self-energy. Dashed lines denote the H bands. Solid lines denote the E bands. All plots show calculations performed at inverse temperature $\beta =100$, $J=U/4,m=3,\lambda =0.3$.