Interaction-driven transition between topological states in a Kondo insulator

Heavy fermion materials naturally combine strong spin-orbit interactions and electronic correlations. When there is precisely one conduction electron per impurity spin, the coherent heavy fermion state is insulating. This Kondo insulating state has recently been argued to belong to the class of quantum spin Hall states. Motivated by this conjecture and a very recent experimental realization of this state, we investigate a model for Kondo insulators with spin-orbit coupling. Using dynamical mean-field theory we observe an interaction-driven transition between two distinct topological states, indicated by a closing of the bulk gap and a simultaneous change of topological invariants as obtained in a classification which takes into account lattice symmetries. At large interaction strength we find a topological heavy fermion state, characterized by strongly renormalized heavy bulk bands, hosting a pair of zero-energy edge modes. The model allows a detailed understanding of the temperature dependence of the single particle spectral function and in particular the energy scales at which one observes the appearance of edge states within the bulk gap.

Figure 1

Phase diagram of the topological Hamiltonian (7) for $t_f=-0.2t$. On the lines where the right-hand side of Eq. (8) evaluates to zero, the topological invariant is not defined, and the system is in a gapless, semimetallic state. The colored, thick lines represent the simulation runs for different ${\varepsilon }_f$ and $U$ and the analytical results at $U=0$ were ${\Sigma }_0=0$. The line color corresponds to the band gap size ${\Delta }_g$. The actual gap closings coincide very well with the predicted transition lines. In a certain part of phase space, instead of the $M$ phase, a possible nontopological Mott phase was found. There the colored lines end. NI denotes the trivial insulator.

Figure 2

Band dispersion for the noninteracting case with open boundaries in the $y$ direction: (a) crossing at $\Gamma$ and (b) crossing at $X$. The position of the crossing depends on the gauge used.

Figure 3

Evolution of the bulk band gap with increasing $U$ for different values of ${\varepsilon }_f$. The solid curves are guides to the eye.

Figure 4

Evolution of the renormalization constant ${\Sigma }_0$ and the effective mass $m_f$ with increasing $U$ for ${\varepsilon }_f=-6.0t$. The horizontal lines indicate the predicted transition lines to the $\Gamma$ phase at ${\Sigma }_0=1.2t$ and the $M$ phase at ${\Sigma }_0=6.0t$ obtained from (8). The solid curves are guides to the eye.

Figure 5

$f$-level occupancy, double occupancy, and the measure of correlation $\Theta$ for ${\varepsilon }_f=-6.0t$ as a function of $U$.

Figure 6

Low energy part of the spectral function for ${\varepsilon }_f=-6.0t$, with an artificial broadening $\delta =0.01$. The interaction strength is (a) $U=5.0t$, which results in band gap of size ${\Delta }_g\approx 0.63t$ and (b) $U=8.2t$ with ${\Delta }_g\approx 0.14t$. Clearly visible is the formation of the heavy, almost flat bands in the strongly correlated case.