GEARS H: Accurate machine-learned Hamiltonians for next-generation device-scale modeling

Abstract

We introduce GEARS H, a state-of-the-art machine-learning Hamiltonian framework for large-scale electronic structure simulations. Using GEARS H, we present a statistical analysis of the hole concentration induced in defective $\mathrm{WSe}_2$ interfaced with Ni-doped amorphous $\mathrm{HfO}_2$ as a function of the Ni doping rate, system density, and Se vacancy rate in 72 systems ranging from 3326 to 4160 atoms-a quantity and scale of interface electronic structure calculation beyond the reach of conventional density functional theory codes and other machine-learning-based methods. We further demonstrate the versatility of our architecture by training models for a molecular system, 2D materials with and without defects, solid solution crystals, and bulk amorphous systems with covalent and ionic bonds. The mean absolute error of the inferred Hamiltonian matrix elements from the validation set is below 2.4 meV for all of these models. GEARS H outperforms other proposed machine-learning Hamiltonian frameworks, and our results indicate that machine-learning Hamiltonian methods, starting with GEARS H, are now production-ready techniques for DFT-accuracy device-scale simulation.