Unitary Transformation of Two-Dimensional Spin-Orbit Coupled Models

Abstract: The Rashba, Dresselhaus, and Weyl Hamiltonians form a foundational framework for modeling spin-orbit interactions across condensed matter systems. Although they describe distinct material classes and produce seemingly different spin textures, they are conventionally treated as separate, unrelated theoretical frameworks. Here, this work demonstrates that the linear 2D Rashba and Weyl models are connected by a specific unitary transformation that maps one Hamiltonian exactly onto the other. The same unitary can be applied to map the linear Dresselhaus-1 model onto the Dresselhaus-2 models and vice versa. Such hidden correspondence establishes a unified theoretical foundation for spin-orbit interactions, deepening our conceptual understanding of spin-orbit coupling and opening new avenues for exploring complex spin textures. To illustrate the application, this work introduces a unique, improved, and more realistic model Hamiltonian H_MKM combining all known foundational spintronic models, where the stringent condition of equal spin-orbit coupling strength of Rashba and Dresselhaus may not be required to observe persistent spin texture under MKM transformation.