# Topological phases and materials

Differently from conventional phase transitions, topological transitions are not characterized by a non-vanishing local order parameter. Rather, they are characterized by a topological index associated to the quantum state, which typically has a straightforward physical interpretation. In the quantum Hall effect, for instance, the topological invariant is associated to the number of edge states and thus emerges in the transversal resistance, which is quantized in terms of universal constants of nature. The discovery of a large class of topological insulators and superconductors has boosted the theoretical modelling of these materials, whose edge/surface states exhibit peculiar properties with quite promising applications in spintronics, nanotechnology and quantum information.

Our group is actively working in this field, and in particular:

- topological and entanglement properties of interacting systems at equilibrium
- electron transport in topological materials
- quantum quenches and far from equilibrium properties of topological systems