Theoretical analysis and high-performance implementation of low-rank approximations in NEGF-based quantum transport

• A novel NEGF-based method is proposed to solve the quantum transport model without large matrix inversions. • A low-rank approximation of the retarded Green’s matrix reduces computational cost. • Rigorous analysis regarding the accuracy of the low-rank approximation is provided. • Finite element discretization is used for the Schrödinger equation and nonlinear Poisson equation in heterogeneous 3D quantum devices. • Numerical simulations show substantial acceleration using CPU and GPU parallelization. The quantum transport model entails a self-consistent coupling between the Schrödinger equation and the nonlinear Poisson equation via the electron density. Among the various steps involved, the computation of the electron density is the most computationally demanding, especially in systems featuring multi-shell quantum dots. In this study, we present a novel and efficient method for computing the electron density within the framework of the non-equilibrium Green’s function (NEGF) approach which circumvents the need for large matrix inversions at each energy level. To further enhance computational efficiency, we incorporate a low-rank approximation technique and provide a rigorous theoretical analysis of its accuracy. Additionally, we show substantial performance improvements in electron density computation through parallel processing on both CPU and GPU architectures.