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

TL;DR

The paper tackles the challenge of predicting Huang–Rhys factors $S$ by introducing a ground-state bonding-character descriptor based on Crystal Orbital Hamilton Population (COHP) to estimate excited-state forces, enabling efficient HR-factor estimation without full excited-state relaxations. Paired with a Ground-Excited Reflective Deformation (GERD) technique, the approach bypasses both explicit excited-state relaxations and full phonon calculations, yielding accurate HR factors from ground-state data. Validation on prototypical defects in monolayer hBN and bulk diamond NV$^{-1}$ demonstrates HR factors spanning $0$ to $20$ and strong agreement with reference calculations, highlighting potential for high-throughput defect screening and rational design of defects as spin qubits and single-photon emitters. The work thus provides a computationally efficient pathway to screen and tailor defect properties via local bonding characteristics, accelerating discovery of optically active defects with targeted electron-phonon coupling.

Abstract

The electron phonon coupling of a defect characterized by its Huang Rhys (HR) factor is a crucial metric determining its excited-state dynamics, relevant to defect applications as qubits and quantum emitters. However, HR factors remain challenging to calculate from first principles, complicated by convergence issues in excited-state relaxation and time consuming phonon calculations. Even when calculated, HR factors lack a rational design principle. Here we show that an orbital-based descriptor can be used to rationalize and efficiently estimate HR factors. Combining this descriptor with a ground state deformation technique allows circumventing both excited state relaxation and full phonon calculations. Specifically, our descriptor for HR factors is constructed using bonding character differences obtained from ground state density functional theory, measured using crystal orbital Hamilton populations. We demonstrate this descriptor for prototypical hBN defects and the diamond NV center. This orbital-based descriptor can be potentially used in high throughput computational screening to identify ideal candidates of spin qubits and SPEs.

Figures (8)

• Figure 1: (a) HR factors can be associated with the change of bonding character between the initial and final states in a given transition. (b) The wavefunctions and the electronic structure of two possible transitions in the V$_\text{B}$O$_\text{N}$$^{-1}$ defect in monolayer h-BN, showing that a smaller HR factor corresponds to a transition involving two states with similar bonding character, both antibonding.
• Figure 2: For the lowest-energy transition in the V$_\text{B}$O$_\text{N}$$^{-1}$ defect, we compare magnitudes of $\vec{F}^{\text{COHP}}$ versus actual $\Delta$SCF forces $\vec{F}^{\text{e}}$. (Top left inset) Full vector plot of $\vec{F}^{\text{COHP}}$
• Figure 3: (a) Total HR factor obtained from full-phonon calculations using real forces compared to ones obtained from COHP-estimated forces . (b) Comparing partial HR factors for the same set of defects and optical transitions.
• Figure 4: (a) Excited-state displacements $\Delta{R}$ obtained via the GERD method and (b) from direct excited-state relaxation with $\Delta$SCF. (c) A schematic of the ground and excited states forces
• Figure 5: Total HR factors obtained from full-phonon calculations using real excited-state forces are used as references (along vertical axis shared across both panels), and compared against HR factors obtained using the GERD method based on (a) real excited-state forces from $\Delta$SCF and (b) COHP-estimated forces. Panel (a) demonstrates the performance of GERD alone; Panel (b) demonstrates the performance of the COHP descriptor combined with GERD.