An order N numerical method to efficiently calculate the transport properties of large systems: An algorithm optimized for sparse linear solvers

JOURNAL OF COMPUTATIONAL PHYSICS

卷:394

Article

Santos, Tatiane R.¹  Lima, Leandro R. F.^1,2  Lewenkopf, Caio H.¹ 

[1] Univ Fed Fluminense, Inst Fis, Av Litoranea S-N, BR-24210346 Niteroi, RJ, Brazil

[2] Univ Fed Rural Rio de Janeiro, Inst Ciencias Exatas, Dept Fis, Rodovia BR-465 Km 07 S-N, BR-23897000 Seropedica, Brazil

关键词: Quantum transport;    Tight-binding approximation;    Wave-function matching;    Scattering matrix;    Multiterminal systems;    Quantum Hall effect;   

DOI  :  10.1016/j.jcp.2019.05.034

来源: Elsevier

【 摘 要 】

We present a self-contained description of the wave-function matching (WFM) method to calculate electronic quantum transport properties of nanostructures using the Landauer-Buttiker 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 linearly with the number of sites, more precisely with similar to N-S x N-P for large N-S, faster than previously claimed. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free