Topological order

Disordered topological materials

Using the topological marker, we elaborate the conditions under which the topological order is invariant in the presence of disorder.

Metric-curvature correspondence

We propose a universal topological invariant for Dirac models in any dimension and symmetry class, and show that it can be measured via a relation with quantum metric that we call metric-curvature correspondence, which also gives rise to the notion of fidelity susceptibility. In addition, this universal topological invariant can be mapped to lattice sites as a universal topological marker. 

Quantum criticality near topological phase transitions

Near topological phase transitions, the curvature function that integrates to the topological invariant generally diverges somewhere in the momentum space. This divergence brings about the notion of renormalization group, critical exponents, correlation functions, and universality classes. This description is true even in weakly interacting and strongly interacting topological materials, and can be used to design an efficient machine learning scheme.

Floquet topological insulators

Periodic driving can be used to engineer fascinating phenomena in topological materials, such as quantum multicriticality in Majorana chain and Chern insulators, as well as crossdimensional universality classes. 

Topological edge states

A defining feature of topological phases of matter, namely the occurrence of the edge state, is found to be true even in the presence of interactions. However, the chiral or helical edge states do not necessarily give an equilibrium edge current.