First-principles analysis of spin relaxation in germanium

Germanium has attracted significant interest for use in quantum technologies owing to its favorable properties such as strong spin-orbit coupling and relatively long spin relaxation times (SRTs). While previous theoretical studies of spin relaxation in Ge have relied on semiempirical models, recent advances have enabled accurate first-principles calculations of SRTs in semiconductors [1,2]. Here we present a first-principles study of spin relaxation in bulk Ge for both electron and hole carriers. We show predictions of T1 SRTs in quantitative agreement with experiment in the 50-350 K temperature range, and analyze the phonon mode- and valley-dependent scattering mechanisms responsible for spin relaxation via the Elliott-Yafet mechanism. Our calculations employ hybrid functionals to describe the electronic structure and obtain accurate e-ph interactions validated by predicting charge transport properties (mobility and velocity-field curves) in close agreement with experiments. The atomistic details obtained with our first-principles approach provide valuable information for designing Ge-based quantum materials and devices.