Strong correlation effects in topological insulators.

Topological quantum phase transitions are characterised by changes in global topological invariants.  These invariants classify many-body systems beyond the conventional paradigm of local order parameters describing spontaneous symmetry breaking. For non-interacting electrons, it is well understood that such transitions are continuous and always accompanied by a gap-closing in the energy spectrum, given that the symmetries protecting the topological phase are maintained. However, most of the topological invariants characterizing topological states are not directly related to makes the identification of experimental fingerprints a key challenge topological phases.

In a recent work we show that new scenarios may arise in strongly correlated systems, due to the interplay between spin, charge and orbital degrees of freedom. In particular, we demonstrated that sufficiently strong electron-electron interaction can fundamentally change the character of the topological transitions. We discovered that a topological quantum phase transition of first-order character, in the genuine thermodynamic sense, occurs without gap closing at strong interaction in a paradigmatic quantum spin Hall insulator system. Our theoretical study reveals the existence of a quantum critical endpoint associated with an orbital instability on the transition line between a 2D topological insulator and a trivial band insulator. Remarkably, this phenomenon entails unambiguous signatures associated to the orbital occupations that can be detected experimentally. 

Phase-diagram of the strongly correlated quantum spin Hall insulator.

We show that, regardless of the value of J, transition between a trivial band insulator and a topological insulator is dominated by the presence of a critical value of U separating a continuous transition from a first-order one. When the Hund's coupling is significant, a 3D Mott insulator is stabilized at large U. In proximity of the Mott transition we observe the emergence of an anomalous “Mott-like” strong topological insulator state.In a subsequent and more recent work we investigated the effects of strong interaction in three-dimensional topological insulators.  

In particular we characterized the evolution of the topological transitions between the different topological phases in 3D as a function of the local Coulomb repulsion U and find a remarkable dependence of the U−M phase diagram on the value of the local Hund's exchange coupling J. ​

Lately, we focused extended our analysis to study the fate of helical edge states in a quantum spin Hall insulators when the whole system is exposed to strong Coulomb interactions. Using dynamical mean-field theory, we show that the dispersion relation of the edge states is strongly affected by Coulomb interactions. In fact, the formerly gapless edge modes become gapped at a critical interaction strength. Interestingly, this critical interaction strength is significantly smaller at the edge than its counterpart in the bulk. Thus, the bulk remains in a topologically nontrivial state at intermediate interaction strengths where the edge states are already gapped out. 

This peculiar scenario leads to the reconstruction of gapless helical states at the new boundary between the topological bulk and the trivial (Mott insulating) edge. Further increasing the interaction strength triggers the progressive localization on the new boundary, the shrinking of the quantum spin Hall region, and the migration of the helical edge states towards the center of the system. The edge state reconstruction process is eventually interrupted by the Mott localization of the whole sample. Finally, we characterize the topological properties of the system by means of a local Chern marker.