Role of Quantum Geometry in the Competition between Higgs Mode and Quasiparticles in Third-Harmonic Generation of Superconductors

TL;DR

This paper reveals that the quantum geometry of electronic bands, especially the quantum metric, plays a crucial role in determining whether the Higgs mode or quasiparticles dominate third-harmonic generation in superconductors, especially in the clean regime.

Contribution

It introduces a formalism incorporating quantum metric into the analysis of THG in superconductors, showing how band geometry can enhance the Higgs mode contribution.

Findings

Quantum metric can significantly amplify Higgs mode coupling.

Large quantum metric can make the Higgs mode dominate THG in clean superconductors.

Band geometry is essential for understanding nonlinear optical responses.

Abstract

Collective modes in superconductors, such as the Higgs mode, offer deep insights into the nature of condensates. Third-harmonic generation (THG) is a primary tool for probing the Higgs mode, but its signal competes with that of quasiparticle excitations depending on impurity scattering rates. In particular, in the clean regime the standard BCS theory generally predicts the dominance of quasiparticle contributions. Here, we propose and demonstrate that the quantum geometry of electronic bands can be a key mechanism governing this competition. By developing a formalism that explicitly incorporates the quantum metric, and applying it to a tunable model of a dispersive-band superconductor, we show that the quantum metric can dramatically amplify the nonlinear light-Higgs coupling by several orders of magnitude. Our results establish that a large quantum metric can cause the Higgs mode to dominate the THG response, resolving the puzzle of Higgs and quasiparticle competition in the clean regime and identifying band geometry as a crucial ingredient for designing and understanding the nonlinear response of superconductors.