Quantum metric and superfluidity

Description

The discovery by Thouless and coworkers of the relation between the quantized Hall conductance and the topological invariant known as the Chern number is a groundbreaking result and the starting point of a fruitful cross-fertilization of ideas between physics and mathematics that continues nowadays. The Chern number in single-particle systems with discrete translational invariance is obtained as the integral of the Berry curvature over the first Brillouin zone. Closely related to the Berry curvature is a less well-known invariant of the band structure called quantum
metric, originally formulated by Provost and Vallee. The quantum metric and the Berry curvature are the real and imaginary part of the quantum geometric tensor, respectively, and therefore they are naturally related to each other. In this talk, I will review the concepts of quantum metric and quantum geometric tensor and explain their relation to the superfluid weight, an important observable quantity for superfluids and superconductors. The contribution to the superfluid weight associated to the quantum metric becomes dominant in the limit of very narrow
bands (flat or quasi-flat bands) and recent theoretical results suggest that it is important to explain the relatively high critical temperature observed in magic angle-twisted bilayer graphene.
Besides twisted bilayer graphene and other moiré materials, which have recently attracted enormous
interest in the condensed matter physics community, I will also outline the prospects for observing
quantum metric-induced superfluidity with ultracold gases in optical lattices [5, 9].

Period	9 Sept 2022
Event title	Solid Math
Event type	Workshop
Conference number	5
Location	Trieste, ItalyShow on map
Degree of Recognition	International