Spin–orbit coupling in silicon for electrons bound to donors

Abstract

Spin–orbit coupling (SOC) is fundamental to a wide range of phenomena in condensed matter, spanning from a renormalisation of the free-electron g-factor, to the formation of topological insulators, and Majorana Fermions. SOC has also profound implications in spin-based quantum information, where it is known to limit spin lifetimes (T1) in the inversion asymmetric semiconductors such as GaAs. However, for electrons in silicon—and in particular those bound to phosphorus donor qubits—SOC is usually regarded weak, allowing for spin lifetimes of minutes in the bulk. Surprisingly, however, in a nanoelectronic device donor spin lifetimes have only reached values of seconds. Here, we reconcile this difference by demonstrating that electric field induced SOC can dominate spin relaxation of donor-bound electrons. Eliminating this lifetime-limiting effect by careful alignment of an external vector magnetic field in an atomically engineered device, allows us to reach the bulk-limit of spin-relaxation times. Given the unexpected strength of SOC in the technologically relevant silicon platform, we anticipate that our results will stimulate future theoretical and experimental investigation of phenomena that rely on strong magnetoelectric coupling of atomically confined spins.