Extracting electron-phonon coupling matrix elements from first principles

Electron-phonon coupling plays an important role in many material systems. While it facilitates useful properties in superconductors, it might be an undesirable mechanism for decoherence in solid state qubits. In this study, we performed first-principles calculations using density functional theory (DFT) as implemented in the Vienna Ab-initio Simulation Package (VASP) and phonon calculations using Phonopy to study the properties of phosphorus-doped silicon. By projecting the Kohn-Sham states onto a local Wannier basis, we are able to examine the extent to which low-energy phonons mix the target phosphorus state with the rest of the environment. This method can be employed to study phonon-driven decoherence in other materials that may be of interest for hosting qubits in a solid-state system.