Quantum Metric Senses A Persistent Spin Helix

TL;DR

This paper shows that the quantum metric can effectively detect and characterize persistent spin helices in systems with balanced spin-orbit coupling, revealing a divergence at the helix condition linked to a hidden degeneracy.

Contribution

It introduces quantum geometry as a novel framework for identifying and analyzing persistent spin helices in spin-orbit coupled systems, including effects of higher-order interactions.

Findings

Quantum metric diverges at the persistent spin helix condition.

Hidden line degeneracy causes the divergence in the quantum metric.

Higher-order cubic spin-orbit interactions regularize the geometric response.

Abstract

Persistent spin helices are a manifestation of symmetry-protected spin textures in systems with balanced spin-orbit coupling. They enable long-lived spin structures that are of interest for spintronics and coherent spin manipulation. The quantum metric has recently emerged as a promising tool for characterizing the geometric structure of quantum states. Here, we demonstrate that the quantum metric provides a sensitive geometric probe of the persistent spin helix. Within the Rashba-Dresselhaus Hamiltonian, we analytically evaluate the quantum metric components and uncover a divergent geometric contribution that emerges precisely at the persistent spin helix condition. We reveal that this divergence originates from a hidden line degeneracy that forms when the strengths of Rashba and Dresselhaus spin-orbit coupling become equal. We further study the role of higher-order cubic spin-orbit interactions and determine how these corrections regularize the geometric response and control the scaling behavior of the quantum metric. Our results establish quantum geometry as a powerful framework for identifying and characterizing persistent spin helices and related symmetry-protected spin textures.