Unified first-principles framework for predicting radiative and non-radiative processes in color centers

Uncovering promising spin-qubit candidates among a myriad of semiconductor point defects requires high-throughput screening based on first-principles calculations. In practice, however, assessing color centers must incorporate phonon-related quantities such as phonon-sideband emission and non-radiative transition rates, which makes the calculations considerably cumbersome. In this paper, we present a method that streamlines the computational steps required to include phonon contributions to both radiative and non-radiative processes. In evaluating the non-radiative transition rate, we simplify the original summation-based expression and obtained a compact, tractable closed-form formula in the low-temperature limit, assuming the electron-phonon coupling matrix element to be constant. Furthermore, we show that perturbative energy evaluations at displaced atomic configurations can be replaced by a much simpler computation of energetics within the single-phonon-mode approximation. We applied the methodology proposed here to impurity-vacancy defects in 4H-SiC and demonstrated that it is highly versatile, allowing straightforward application to a broad range of material systems beyond those examined in this study.