Graph neural networks (GNNs) have shown promise in learning the ground-state electronic properties of materials, subverting ab initio density functional theory (DFT) calculations when the underlying lattices can be represented as small and/or repeatable unit cells (i.e., molecules and periodic crystals). Realistic systems are, however, non-ideal and generally characterized by higher structural complexity. As such, they require large (10+ {Å}) unit cells and thousands of atoms to be accurately described. At these scales, DFT becomes computationally prohibitive, making GNNs especially attractive. In this work, we present a strictly local equivariant GNN capable of learning the electronic Hamiltonian (H) of realistically extended materials. It incorporates an augmented partitioning approach that enables training on arbitrarily large structures while preserving local atomic environments beyond boundaries. We demonstrate its capabilities by predicting the electronic Hamiltonian of various systems with up to 3,000 nodes (atoms), 500,000+ edges, 28 million orbital interactions (nonzero entries of H), and $\leq$0.53% error in the eigenvalue spectra. Our work expands the applicability of current electronic property prediction methods to some of the most challenging cases encountered in computational materials science, namely systems with disorder, interfaces, and defects.

Designing nanoscale electronic devices such as the currently manufactured nanoribbon field-effect transistors (NRFETs) requires advanced modeling tools capturing all relevant quantum mechanical effects. State-of-the-art approaches combine the non-equilibrium Green’s function (NEGF) formalism and density functional theory (DFT). However, as device dimensions do not exceed a few nanometers anymore, electrons are confined in ultra-small volumes, giving rise to strong electron-electron interactions. To account for these critical effects, DFT+NEGF solvers should be extended with the GW approximation, which massively increases their computational intensity. Here, we present the first implementation of the NEGF+GW scheme capable of handling NRFET geometries with dimensions comparable to experiments. This package, called QuaTrEx, makes use of a novel spatial domain decomposition scheme, can treat devices made of up to 84,480 atoms, scales very well on the Alps and Frontier supercomputers (> 80% weak scaling efficiency), and sustains an exascale FP64 performance on 42,240 atoms (1.15 Eflop/s).

Experimental development of gate-all-around silicon nanowire field-effect transistors (NWFETs), a viable replacement for FinFETs, can be complemented by technology computer-aided design. This requires the availability of advanced device simulators relying on a quantum transport (QT) approach without any empirical parameters as inputs. Concretely, all material properties should be described from first-principles, and the whole physics at play should be accurately modeled, particularly the strong electron-electron interactions occurring in highly confined structures such as NWFETs. To shed light on these many-body effects, we implement them within the self-consistent GW approximation into an ab initio QT solver called QuaTrEx, based on density functional theory and the Non-equilibrium Green’s Function formalism. We then simulate transistors made of up to 10,560 atoms on the LUMI supercomputer’s GPU partition, reaching a parallel efficiency of $\mathbf{7 4 \%}(\mathbf{6 0 \%}$) in weak (strong) scaling and an overall computational performance of 69.3 Pflop/s in double precision on 1,800 nodes.

Simulating emerging resistive switching memory devices, such as memristors, requires modeling frameworks that can treat the motion of point defects across nanoscale domains. Field-driven Kinetic Monte Carlo (d-KMC) methods that simulate the discrete structural evolution of atomic coordinates in the presence of external potential and heat fields can be used for this purpose. While physically similar to conventional KMC methods, field-driven approaches present different computational motifs and introduce global communication. Here, we develop the first scalable d-KMC code for resistive memory arrays at atomistic resolution. We accelerate this latency-sensitive simulation on the GPU partition of the LUMI Supercomputer, exploiting the high-speed interconnects between GPUs on the same node. Applied to the technologically relevant HfOx material stack, our code enables the first atomistic simulation of $3 \times 3$ arrays of resistive switching memory cells with more than 1 million atoms, matching the dimensions of fabricated structures.