Rational design of defect qubits with small Huang-Rhys factors using bonding character as a descriptor

The electron-phonon coupling of a defect qubit – characterized by its Huang–Rhys (HR) factor – is a crucial metric determining the excited-state dynamics, optical control, and readout of the defect qubit. However, first-principles computation of HR factors is often complicated by convergence issues in modeling excited-state forces and time-consuming phonon calculations. Here we propose an orbital-based descriptor for HR factors to circumvent full excited-state calculations, and a force-based 1D effective phonon model that requires neither a full phonon calculation nor excited-state relaxations. This approximation of calculating HR factors enables the development of a rational design principle for engineering defect qubits and single-photon emitters.

Specifically, our descriptor for HR factors is constructed using the degree of bonding-character difference obtained from ground-state density functional theory, measured using Crystal Orbital Hamiltonian Populations (COHP). We demonstrate this descriptor for multiple optical transitions in realistic qubit candidates in hBN defect systems and the NV– center in diamond. Reference HR factors are first calculated using excited-states forces (from constrained DFT) and phonons from first-principles, where basic defect properties (e.g. spectral functions) are carefully converged towards the dilute limit using an embedding method for force constants. COHP-based descriptors for HR factors are then constructed, and obtained for the same set of defects to assess their accuracy. We show that our descriptor-based partial and summed HR factors are highly correlated with reference HR factors from full calculations. Using only ground-state properties to quantify electron-phonon coupling, the COHP-based descriptor can be potentially used in high-throughput computation for identifying ideal candidates of defect qubits.