Floquet-engineering of nodal rings and nodal spheres and their characterization using the quantum metric

TL;DR

This paper proposes a method to realize and characterize nodal rings and spheres in synthetic quantum systems using Floquet engineering, with quantum metric measurements serving as key signatures of their topological properties.

Contribution

It introduces a Floquet-based scheme to create nodal defects and demonstrates how quantum metric measurements can detect their topological features.

Findings

Quantum metric signatures reveal nodal rings without Berry curvature.

Quantum metric measurements can detect topological charge of nodal spheres.

Experimental protocols for Floquet nodal defects in atomic systems are proposed.

Abstract

Semimetals exhibiting nodal lines or nodal surfaces represent a novel class of topological states of matter. While conventional Weyl semimetals exhibit momentum-space Dirac monopoles, these more exotic semimetals can feature unusual topological defects that are analogous to extended monopoles. In this work, we describe a scheme by which nodal rings and nodal spheres can be realized in synthetic quantum matter through well-defined periodic-driving protocols. As a central result of our work, we characterize these nodal defects through the quantum metric, which is a gauge-invariant quantity associated with the geometry of quantum states. In the case of nodal rings, where the Berry curvature and conventional topological responses are absent, we show that the quantum metric provides an observable signature for these extended topological defects. Besides, we demonstrate that quantum-metric measurements could be exploited to directly detect the topological charge associated with a nodal sphere. We discuss possible experimental implementations of Floquet nodal defects in few-level atomic systems, paving the way for the exploration of Floquet extended monopoles in quantum matter.