A numerical method to efficiently calculate the transport properties of large systems: an algorithm optimized for sparse linear solvers

Abstract

We present a self-contained description of the wave-function matching (WFM) method to calculate electronic quantum transport properties of nanostructures using the Landauer-Büttiker approach. The method is based on a partition of the system between a central region ("conductor") containing $N_S$ sites and an asymptotic region ("leads") characterized by $N_P$ open channels. The two subsystems are linearly coupled and solved simultaneously using an efficient sparse linear solver. Invoking the sparsity of the Hamiltonian matrix representation of the central region, we show that the number of operations required by the WFM method in conductance calculations scales with $\sim N_S\times N_P$ for large $N_S$.

arXiv comment22 pages, 8 figures

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• Linear Scaling Quantum Transport Methodologies
• Crystallographic Characterization of Black Phosphorene and Its Application in Nanostructures
• Efficient numerical method for evaluating normal and anomalous time-domain equilibrium Green's functions in inhomogeneous systems
• Simulating time-dependent thermoelectric transport in quantum systems
• Edge and sublayer degrees of freedom for phosphorene nanoribbons with twofold-degenerate edge bands via electric field
• Fabry-Pérot resonant vortices and magnetoconductance in topological insulator constrictions with magnetic barriers
• Local equilibrium charge and spin currents in two-dimensional topological systems
• Improved performance in quantum transport calculations: A divide-and-conquer method based on S-matrices