"One defect, one potential" strategy for accurate machine learning prediction of defect phonons

TL;DR

This paper tackles the computational bottleneck of defect-phonon calculations in large solids by introducing a defect-specific MLIP framework, "one defect, one potential." Using NequLP Allegro, it trains a small, defect-centered model on ~40 perturbed structures to predict forces with high fidelity, enabling accurate phonon frequencies, eigenvectors, and Huang-Rhys factors that match DFT across 96- and 360-atom cells. The authors demonstrate the approach's utility in predicting radiative PL lineshapes and nonradiative multiphonon transition rates, achieving near-DFT accuracy while reducing computational cost by orders of magnitude, and extend its reach to large-scale embedding schemes up to ~10^4 atoms. This work provides a practical pathway for high-accuracy, large-scale defect phonon studies and paves the way for high-throughput predictions of defect-related vibrational phenomena in technologically relevant materials.

Abstract

Atomic vibrations play a critical role in phonon-assisted electron transitions at defects in solids. However, accurate phonon calculations in defect systems are often hindered by the high computational cost of large-supercell first-principles calculations. Recently, foundation models, such as universal machine learning interatomic potentials (MLIPs), emerge as a promising alternative for rapid phonon calculations, but the quantitatively low accuracy restricts its fundamental applicability for high-level defect phonon calculations, such as nonradiative carrier capture rates. In this paper, we propose a "one defect, one potential" strategy in which an MLIP is trained on a limited set of perturbed supercells. We demonstrate that this strategy yields phonons with accuracy comparable to density functional theory (DFT), regardless of the supercell size. The predicted accuracy of defect phonons is validated by phonon frequencies, Huang-Rhys factors, and phonon dispersions. Further calculations of photoluminescence (PL) spectra and nonradiative capture rates based on this defect-specific model also show good agreements with DFT results, meanwhile reducing the computational expenses by more than an order of magnitude. Our approach provides a practical pathway for studying defect phonons in 10$^4$-atom large supercell with high accuracy and efficiency.

Figures (4)

• Figure 1: Workflow of accelerating phonon calculations through MLIP. The method is based on the finite displacement method, uses MLIP to predict forces.
• Figure 2: Benchmarking the phonon prediction accuracy of the MLIP against DFT for neutral ($\text{C}_\text{N}^0$) and negatively charged ($\text{C}_\text{N}^{-}$) defects in 96-atom and 360-atom supercells. (a) Comparison of phonon frequencies between MLIP and DFT. The frequencies of the $\text{C}_\text{N}^{-}$ defect predicted by MLIP are shifted upward by 20 meV along the vertical axis. (b) Comparison of the Huang-Rhys factors $S_k$. (c)-(f) Unfolded phonon band structures and densities of states (DOS) projected onto the primitive cell (4 atoms). In the phonon band structures, red lines denote MLIP predictions, while blue lines represent DFT results. In the DOS plots, red dashed lines correspond to MLIP, and blue solid lines to DFT.
• Figure 3: Application of MLIP-accelerated phonon calculations. (a) Schematic of constructing force constants in a large supercell using MLIP. The yellow circle represents the defect site, the transparent blue circular region indicates the cut-off radius $r_d$ around the defect supercell, and the transparent blue square marks the boundary $r_b$ beyond which MLIP predictions are truncated to zero. (b) Convergence test of the Huang-Rhys factors $S_k$ and spectral function $S(\hbar\omega)$ of the $\text{C}_{\text{N}}$ defect as a function of supercell size. (c) Radiative PL lineshapes calculated for different supercell sizes; blue dashed lines indicate DFT results. In (b) and (c), the 96-atom and 360-atom supercells are computed using MLIPs trained on cells of the same size, while larger supercells are constructed using the embedding approach shown in (a). (d) Nonradiative capture coefficient $C_p$ of the $\text{C}_{\text{N}}$ defect as a function of temperature $T$ and transition energy $\Delta E$. Dashed lines represent MLIP predictions, solid lines correspond to DFT calculations, red lines are computed using the initial-state basis, blue lines with the final-state basis, and the purple star denotes the experimental value.
• Figure 4: Comparison of the total computational time required for a full phonon calculation using either DFT or MLIP across different supercell sizes. Blue solid lines represent quartic fits of the form $AN^4$, and red solid lines correspond to cubic fits of the form $BN^3$, with $A$ and $B$ as fitting parameters. The left panel shows results using the PBE functional, while the right panel uses the HSE functional.