Rashba-like spin splitting around non-time-reversal-invariant momenta

Abstract

The ubiquitous Rashba spin splitting occurring around time-reversal-invariant momenta (TRIM) reflects the fundamental interplay between spin-orbit coupling (SOC) and crystalline symmetry. Unexpectedly, recent measurements reveal novel Rashba spin splitting around the momenta lacking time-reversal symmetry (non-TRIM), whose mechanism remains elusive. Here, we theoretically elucidate the microscopic origin of Rashba spin splitting around non-TRIM and identify the design principles for its appearance. Conventionally, a Zeeman-like spin splitting dominates around non-TRIM due to the broken time-reversal symmetry and diminishes the Rashba-like features. Our results show that the Bloch wave function with specific orbital representation at certain non-TRIM could eliminate the first-order SOC effect. As a result, the corresponding little group hosts a type of quasisymmetry that commutes with the dominating SOC Hamiltonian, leading to a tiny SOC gap and helical spin texture. Furthermore, such a quasi-symmetry-induced tiny gap could manifest large Berry curvature, which is desirable for various topological applications. Our work expands the concept of Rashba physics beyond the conventional TRIM scenario, paving an avenue for designing novel spin-splitting materials through the cooperation of symmetry and orbital engineering.