# On the pseudospin description of the electron Bloch bands

## TL;DR

This paper critically examines the pseudospin-1/2 model for electron Bloch bands with spin-orbit coupling, providing a symmetry-consistent basis construction and deriving generalized Rashba Hamiltonians for noncentrosymmetric crystals.

## Contribution

It introduces a symmetry-based method for constructing Bloch bases and derives more accurate effective Hamiltonians beyond the traditional pseudospin approximation.

## Key findings

- Identifies limitations of the pseudospin-1/2 description.
- Provides a systematic basis construction using magnetic point group corepresentations.
- Derives generalized Rashba models for complex crystal symmetries.

## Abstract

We study the transformation properties of the electron states in crystals with spin-orbit coupling, focusing primarily on the limitations of the frequently used pseudospin-1/2 description of twofold degenerate Bloch bands. Using the language of corepresentations of magnetic point groups, we construct the Bloch bases across the Brillouin zone in a way which is consistent with all symmetry requirements. This construction is applied to derive the effective spin-orbit Hamiltonians in noncentrosymmetric crystals, known as the generalized Rashba models, in both single-band and multiband cases.