Floquet quantum geometry in periodically driven topological insulators

TL;DR

This paper introduces a time-resolved quantum metric tensor framework for Floquet topological insulators, revealing a fundamental link between quantum geometry and topology in periodically driven systems.

Contribution

It proposes a novel quantum geometric tensor in Floquet systems and establishes a lower bound relating quantum volume to topological invariants.

Findings

Quantum volume is bounded below by Floquet topological invariants.

The framework applies to class A in 2D and class AIII in 1D systems.

Time-reflection symmetry can reduce the Floquet geometric tensor.

Abstract

Quantum geometry plays a fundamental role across many branches of modern physics, yet its full characterization in nonequilibrium systems remains a challenge. Here, we propose a framework for quantum geometry in Floquet topological insulators by introducing a time-resolved quantum metric tensor, defined via the trace distance between micromotion operators in momentum-time space. For class A in two spatial dimensions, we find a general inequality linking the Floquet quantum metric tensor and the Floquet topology: the associated quantum volume is bounded below by the Floquet topological invariant. This relation is found to also hold in class AIII in one dimension, where the Floquet geometric tensor may be notably reduced due to time-reflection symmetry. This work will be useful in digesting the general aspects of quantum geometry in periodically driven systems in connection with their topological characterization.