Correlation Effects on 3D Topological Phases: From Bulk to Boundary

Topological phases of quantum matter defy characterization by conventional order parameters but can exhibit a quantized electromagnetic response and/or protected surface states. We examine such phenomena in a model for three-dimensional correlated complex oxides, the pyrochlore iridates. The model realizes interacting topological insulators, with and without time-reversal symmetry, and topological Weyl semimetals. We use cellular dynamical mean-field theory, a method that incorporates quantum many-body effects and allows us to evaluate the magnetoelectric topological response coefficient in correlated systems. This invariant is used to unravel the presence of an interacting axion insulator absent within a simple mean-field study. We corroborate our bulk results by studying the evolution of the topological boundary states in the presence of interactions. Consequences for experiments and for the search for correlated materials with symmetry-protected topological order are given.

Figure 1

Magnetization ($m$) and topological index ($\Delta$) versus interaction strength. An interaction-driven topological transition accompanies an abrupt change of the magnetization. In the intermediate region, a topologically nontrivial insulator with a finite magnetization indicates the realization of an interacting axion insulator (AI). As the interaction strength increases, a TWS appears after the magnetization jump. At large $U$, the system is a topologically trivial AFI. The magnetic structure is illustrated in the inset.

Figure 2

Surface states of a slab normal to (110). (a) First BZ of a pyrochlore lattice and its projection onto the (110)-surface BZ. (b) Spectral weight at the Fermi level, $\omega =0$, for the TWS with $U/t=4.7$. Fermi arcs crossing $k_y=0$ clearly appear. The position of the arcs is roughly consistent with the HF result, denoted by lines in the middle of the arc features. (c) Density plot of the surface spectral functions along lines connecting high symmetry points. From left to right, the panels represent a TI, a TWS, and an AFI. The inset shows more clearly the surface states of the TWS near the Fermi level, $\omega =0$.

Figure 3

Spectral weights along high symmetry lines and local density of states for different values of $U/t$. The panels represent a TI, a TWS, and an AFI. These last two phases break TRS. In the TWS, the Weyl points are not along high symmetry lines, but the density of states shows a quadratic scaling indicating their presence, as shown by the arrow.