Machine-Learned Hamiltonians for Quantum Transport Simulation of Valence Change Memories

The construction of the Hamiltonian matrix $\mathbf{H}$ is an essential, yet computationally expensive step in ab-initio device simulations based on density-functional theory (DFT). In homogeneous structures, the fact that a unit cell repeats itself along at least one direction can be leveraged to minimize the number of atoms considered and the calculation time. However, such an approach does not lend itself to amorphous or defective materials for which no periodicity exists. In these cases, (much) larger domains containing thousands of atoms might be needed to accurately describe the physics at play, pushing DFT tools to their limit. Here we address this issue by learning and directly predicting the Hamiltonian matrix of large structures through equivariant graph neural networks and so-called augmented partitioning training. We demonstrate the strength of our approach by modeling valence change memory (VCM) cells, achieving a Mean Absolute Error (MAE) of 3.39 to 3.58 meV, as compared to DFT, when predicting the Hamiltonian matrix entries of systems made of $\sim 5,000$ atoms. We then replace the DFT-computed Hamiltonian of these VCMs with the predicted one to compute their energy-resolved transmission function with a quantum transport tool. A qualitatively good agreement between both sets of curves is obtained. Our work provides a path forward to overcome the memory and computational limits of DFT, thus enabling the study of large-scale devices beyond current ab-initio capabilities.