Tight-binding Rashba model and statistical field theory

TL;DR

This paper provides a pedagogical review of the tight-binding Rashba model on a hexagonal lattice, deriving spin splitting from symmetry and discussing Green functions and renormalization group equations.

Contribution

It introduces a minimal tight-binding model for Rashba spin splitting and details the symmetry and Green function conventions used in the analysis.

Findings

Derived Rashba spin splitting from symmetry conditions

Constructed a minimal tight-binding Rashba model

Summarized Green function properties and RG equations

Abstract

This document contains information supplementary to the article [1], but it is self-contained and can be read independently as a pedagogical review. In the first part, we explain our conventions for the tight-binding description of electronic states on the hexagonal Bravais lattice in two dimensions. We derive the Rashba spin splitting from elementary symmetry conditions, and subsequently construct a minimal tight-binding model which displays Rashba spin splitting near the center of the Brillouin zone. Furthermore, we derive the corresponding symmetry conditions for a two-particle interaction in a second-quantized framework. In the second part, we describe our conventions for the temperature Green functions, in terms of which the renormalization group equations in [1] have been formulated. We also provide a brief summary of the most important definitions and properties of temperature Green functions. [1] G. A. H. Schober, K.-U. Giering, M. M. Scherer, C. Honerkamp, and M. Salmhofer, arXiv:1409.7087.