Quantum Geometry in Quantum Materials

TL;DR

This review introduces quantum geometry in quantum materials, emphasizing its fundamental role in various physical phenomena and its potential for future research directions.

Contribution

It provides an accessible overview of quantum geometry's implications across multiple domains in quantum materials, highlighting its significance and open questions.

Findings

Quantum geometry influences optical responses and Landau levels.

It plays a role in fractional Chern insulators and superfluid weight.

The field has numerous open questions and future research directions.

Abstract

Quantum geometry, characterized by the quantum geometric tensor, is pivotal in diverse physical phenomena in quantum materials. In condensed matter systems, quantum geometry refers to the geoemtric properties of Bloch states in the Brillouin zone. This pedagogical review provides an accessible introduction to the concept of quantum geometry, emphasizing its extensive implications across multiple domains. Specifically, we discuss the role of quantum geometry in optical responses, Landau levels, and fractional Chern insulators, as well as its influence on superfluid weight, spin stiffness, exciton condensates, electron-phonon coupling, etc. By integrating these topics, we underscore the pervasive significance of quantum geometry in understanding emergent behaviors in quantum materials. Finally, we present an outlook on open questions and potential future directions, highlighting the need for continued exploration in this rapidly developing field.