Renormalization group study of intervalley scattering and valley splitting in a two-valley system

TL;DR

This paper derives renormalization group equations for a two-valley system considering valley splitting and intervalley scattering, revealing a third relevant scaling parameter that influences finite-temperature behavior.

Contribution

It introduces a third scaling parameter into the two-parameter renormalization group theory for two-valley systems, enhancing understanding of valley splitting effects.

Findings

A third relevant scaling parameter affects finite-temperature behavior.

Qualitative conclusions of the two-parameter theory remain valid.

Quantitative behavior is modified at finite temperatures.

Abstract

Renormalization group equations are derived for the case when both valley splitting and intervalley scattering are present in a two-valley system. A third scaling parameter is shown to be relevant when the two bands are split but otherwise distinct. The existence of this parameter changes the quantitative behavior at finite temperatures, but the qualitative conclusions of the two-parameter theory are shown to be unaffected for realistic choice of parameters.