What happens to geometric phase when spin-orbit interactions lift band degeneracy?

TL;DR

This paper investigates how spin-orbit interactions affect the geometric phase around band degeneracies, showing that the phase can change or remain depending on the spin fixation during adiabatic evolution.

Contribution

It reveals the dependence of the geometric phase on spin fixation in systems with lifted band degeneracy due to spin-orbit interaction.

Findings

Gamma(C) decreases to zero when spin is fixed along the internal spin-orbit field.

Gamma(C) remains pi when spin is fixed perpendicular to the internal field.

The behavior of the geometric phase depends on the spin fixation during adiabatic evolution.

Abstract

Spin-orbit interaction lifts accidental band degeneracy. The geometric phase gamma(C)=pi for circuits surrounding a line of such degeneracy cannot survive completely unchanged. The change depends on how the spin is fixed during adiabatic evolution. For spin fixed along the internal spin-orbit field, gamma(C) decreases to zero as the circuit collapses around the line of lifted degeneracy. For spin fixed along a perpendicular axis, the conical intersection persists and gamma(C)=pi is unchanged.