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

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.