Improved recursive Green's function formalism for quasi one-dimensional systems with realistic defects

• Published in: Journal of computational physics Vol. 334; pp. 607 - 619
• Main Authors: Teichert, Fabian, Zienert, Andreas, Schuster, Jörg, Schreiber, Michael
• Format: Journal Article
• Language: English
• Published: Cambridge Elsevier Inc 01.04.2017; Elsevier Science Ltd
• Subjects: Algorithms; Carbon nanotube (CNT); Carbon nanotubes; Computational mathematics; Computational physics; Defect; Defects; Electronic transport; Formalism; Green's functions; Iterative methods; Mathematical analysis; Nanotubes; Quantum theory; Quantum transport; Recursive functions; Recursive Green's function formalism (RGF); Renormalization decimation algorithm (RDA); Studies; Transport theory; Carbon nanotube (CNT); Defect; Renormalization decimation algorithm (RDA); Recursive Green's function formalism (RGF); Electronic transport
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2017.01.024

We derive an improved version of the recursive Green's function formalism (RGF), which is a standard tool in the quantum transport theory. We consider the case of disordered quasi one-dimensional materials where the disorder is applied in form of randomly distributed realistic defects, leading to partly periodic Hamiltonian matrices. The algorithm accelerates the common RGF in the recursive decimation scheme, using the iteration steps of the renormalization decimation algorithm. This leads to a smaller effective system, which is treated using the common forward iteration scheme. The computational complexity scales linearly with the number of defects, instead of linearly with the total system length for the conventional approach. We show that the scaling of the calculation time of the Green's function depends on the defect density of a random test system. Furthermore, we discuss the calculation time and the memory requirement of the whole transport formalism applied to defective carbon nanotubes. With the improved recursive Green's function formalism + renormalization decimation algorithm (RGF+RDA), the conductance of mesoscopic systems with realistic defects can be computed much faster than with the common RGF. For a constant system length, the calculation time t scales logarithmically with the number of defects ND. This is true for the recursive decimation scheme (RDS) as well as for the forward iteration scheme (FIS). •An improved version of the recursive Green's function formalism is derived.•Transport calculations for carbon nanotubes with realistic defects are faster.•The calculation time is reduced by up to 80% for systems with 1% defects.