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.
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BibTeX
@misc{liu2026linearscaling,
title = {{Linear-Scaling Quantum Transport from Machine-Learning Density Functional Theory Hamiltonians}},
author = {Bang Liu and Yang Zhong and Zhi-Xin Guo and Xin-Gao Gong and Hongjun Xiang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.37058},
eprint = {2609.37058},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.37058},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Linear-Scaling Quantum Transport from Machine-Learning Density Functional Theory Hamiltonians
AU - Bang Liu
AU - Yang Zhong
AU - Zhi-Xin Guo
AU - Xin-Gao Gong
AU - Hongjun Xiang
PY - 2026
DA - 2026/09/29
PB - arXiv
DO - 10.48550/arxiv.2609.37058
UR - https://arxiv.org/abs/2609.37058
AB - 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.
ER -