Linear-Scaling Quantum Transport from Machine-Learning Density Functional Theory Hamiltonians

Abstract

Quantum transport simulations that combine density functional theory (DFT) with the nonequilibrium Green's function formalism (DFT-NEGF) are important to modern technology, yet their unfavorable scaling has long confined predictive simulations to small, idealized systems far below the ten-thousand-atom scale of realistic devices. Here, we introduce HamGNN-NEGF, a linear-scaling framework with DFT-level fidelity. An E(3)-equivariant graph neural network trained on conventional DFT Hamiltonians of small structures predicts Hamiltonians for large devices, avoiding costly DFT-NEGF training data. The predicted Hamiltonians are integrated with DFT-derived electrode self-energies, a nonorthogonal kernel polynomial method for Fermi-level determination, and a recursive Green's function algorithm, yielding a computational cost that scales linearly with device length at fixed cross section. Even for devices containing fewer than 500 atoms, HamGNN-NEGF achieves speedups exceeding three orders of magnitude over fully self-consistent DFT-NEGF, with the advantage increasing further with system size. Benchmarks on pristine Pt-Si-Pt, doped Pt-Si:P-Pt, and Pt-molecule-Pt junctions demonstrate meV-level Hamiltonian accuracy, faithful transmission spectra, and predictive simulations beyond 10,000 atoms. Eliminating transport self-consistency also enables hybrid functionals such as HSE06 without additional NEGF overhead, while a zero-bias Hamiltonian approximation extends the framework to finite-bias transport in weakly nonlinear regimes. HamGNN-NEGF thus bridges first-principles accuracy and device-scale simulation, providing a practical route toward predictive modeling of realistic nanoelectronic and quantum devices.