Unitary Transformation of Two-Dimensional Spin-Orbit Coupled Models

TL;DR

This paper reveals a unitary transformation linking different 2D spin-orbit models, unifying their theoretical framework and enabling new insights into spin textures and spintronic applications.

Contribution

It demonstrates that Rashba, Dresselhaus, and Weyl models are connected via a specific unitary transformation, unifying their descriptions of spin-orbit interactions.

Findings

Linear Rashba and Weyl models are exactly connected by a unitary transformation.

Dresselhaus-1 and Dresselhaus-2 models can be mapped onto each other similarly.

A new comprehensive Hamiltonian model combines all foundational spintronic 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.