Bonding Character as a Descriptor for Huang-Rhys Factors in Optically Active Defects

The electron-phonon coupling of optical transitions in a defect is a crucial metric for describing the defect’s utility for quantum applications, typically characterized by a Huang-Rhys (HR) factor. For a spin qubit, the HR factor is needed for phonon-assisted nonradiative recombination rates; for a single-photon emitter, the HR factor determines the degree of photon indistinguishability. Computing HR factors is a complex task that requires excited-state dynamics and time-consuming phonon calculations. Therefore, it is highly desirable to establish an efficient descriptor for HR factors based solely on ground-state defect properties. Building such a descriptor will enable the development of a rational design principle for engineering defects-based SPEs and qubits.

We construct such a descriptor for HR factors by approximating excited state forces using the degree of bonding-character difference obtained from ground-state density functional theory, measured using Crystal Orbital Hamiltonian Populations (COHP). We propose that small HR factors are linked to the similarity of bonding character between the initial (occupied) and final (unoccupied) states in a given excitation. We demonstrate this descriptor for multiple optical transitions in realistic SPE candidates in hBN defect systems and the NV center in diamond. Reference HR factors are first calculated using excited-states forces and phonons from first-principles, where basic defect properties (e.g. spectral function) 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 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 defects that serve as ideal candidates for qubits and SPEs.