Quantum Phonon Dynamics Induced Spontaneous Spin-Orbit Coupling

TL;DR

This paper demonstrates that spin-orbit coupling can spontaneously arise from electron-phonon interactions through symmetry breaking, revealing new phases and transitions in a model system, with implications for spintronics materials.

Contribution

It introduces a model showing spontaneous spin-orbit coupling from symmetry breaking, supported by quantum Monte Carlo simulations, expanding understanding of spin-orbit phenomena beyond single-particle effects.

Findings

Spin-orbit coupling emerges as an order in the ground state in the adiabatic limit.

A breathing mode of lattice distortion and staggered loop spin-current accompany the phase.

Phase transition to charge-density-wave or superconductivity occurs at high phonon frequency and coupling.

Abstract

Spin-orbit coupling in solids is typically a single-body effect arising from relativity. In this work, we propose a spontaneous generation of spin-orbit coupling from symmetry breaking. A spin-dependent electron-phonon coupling model is investigated on a half-filled square lattice, which is solved by sign-problem-free quantum Monte Carlo simulations. The phase diagram as function of phonon frequency $\omega$ and coupling constant $\lambda$ is fully investigated. The spin-orbit coupling emerges as an order in the ground state for any $\lambda$ in the adiabatic limit, accompanied by a breathing mode of lattice distortion and a staggered loop spin-current. This phase dominates in the entire range of $\omega$ with $\lambda< \lambda_{\infty}$, a critical value in the $\omega \to \infty$ limit. With increasing $\omega$ and $\lambda > \lambda_{\infty}$, the emergent spin-orbit coupling is suppressed and a phase transition occurs leading to charge-density-wave degenerate with superconductivity order. Our work opens up the possibility of hidden spin-orbit coupling in materials where it is otherwise forbidden by lattice symmetry and paves the way to explore new usable materials or devices in spintronics.