Reduction of Topological Z Classification in Cold-Atom Systems

Higher-Order Topological Mott Insulators

We propose a new correlated topological state, which we call a higher-order topological Mott insulator (HOTMI). This state exhibits a striking bulk-boundary correspondence due to electron correlations. Namely, the topological properties in the bulk, characterized by the Z_{3} spin-Berry phase, result in gapless corner modes emerging only in spin excitations (i.e., the single-particle excitations remain gapped around the corner). We demonstrate the emergence of the HOTMI in a Hubbard model on the kagome lattice, and elucidate how strong correlations change gapless corner modes at the noninteracting case.

Interacting topological insulators: a review

The discovery of the quantum spin Hall effect and topological insulators more than a decade ago has revolutionized modern condensed matter physics. Today, the field of topological states of matter is one of the most active and fruitful research areas for both experimentalists and theorists. The physics of topological insulators is typically well described by band theory and systems of non-interacting fermions. In contrast, several of the most fascinating effects in condensed matter physics merely exist due to electron-electron interactions, examples include unconventional superconductivity, the Kondo effect, and the Mott-Hubbard transition. The aim of this review article is to give an overview of the manifold directions which emerge when topological bandstructures and correlation physics interfere and compete. These include the study of the stability of topological bandstructures and correlated topological insulators. Interaction-induced topological phases such as the topological Kondo insulator provide another exciting topic. More exotic states of matter such as topological Mott insulator and fractional Chern insulators only exist due to the interplay of topology and strong interactions and do not have any bandstructure analogue. Eventually the relation between topological bandstructures and frustrated quantum magnetism in certain transition metal oxides is emphasized.