Quantum Metric and Correlated States in Two-dimensional Systems

TL;DR

This paper reviews how the quantum metric of electronic bands influences correlated states like superconductivity in twisted bilayer graphene, highlighting the tunability of these states via the twist angle.

Contribution

It establishes a theoretical and experimental link between quantum metric and properties of correlated states, especially superfluid stiffness, in two-dimensional twisted bilayer systems.

Findings

Quantum metric affects superfluid stiffness in twisted bilayer graphene.

Tuning twist angle controls band flatness and quantum metric.

Correlation between quantum metric and superconducting properties is demonstrated.

Abstract

The recent realization of twisted, two-dimensional, bilayers exhibiting strongly correlated states has created a platform in which the relation between the properties of the electronic bands and the nature of the correlated states can be studied in unprecedented ways. The reason is that these systems allow extraordinary control of the electronic bands' properties, for example by varying the relative twist angle between the layers forming the system. In particular, in twisted bilayers the low energy bands can be tuned to be very flat and with a nontrivial quantum metric. This allows the quantitative and experimental exploration of the relation between the metric of Bloch quantum states and the properties of correlated states. In this work we first review the general connection between quantum metric and the properties of correlated states that break a continuous symmetry. We then discuss the specific case when the correlated state is a superfluid and show how the quantum metric is related to the superfluid stiffness. To exemplify such relation we show results for the case of superconductivity in magic angle twisted bilayer graphene. We conclude by discussing possible research directions to further elucidate the connection between quantum metric and correlated states' properties.