Parallel implementation of the recursive Green’s function method

Drouvelis, P. S.; Schmelcher, Peter; Bastian, Peter

doi:10.1016/j.jcp.2005.11.010

Cited by 29 publications

(36 citation statements)

References 19 publications

(21 reference statements)

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“…From this GF both transport and local properties can be obtained. However, for most purposes we do not require every element of the GF matrix element in the device region, and so to avoid a timeconsuming, full-matrix inversion, various recursive or other decomposition methods are often applied [9,14,20,[25][26][27][28][29][30][31][32].…”

Section: Adaptive Recursion For Device Regionmentioning

confidence: 99%

Patched Green's function techniques for two-dimensional systems: Electronic behavior of bubbles and perforations in graphene

et al. 2015

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We present a numerically efficient technique to evaluate the Green's function for extended two dimensional systems without relying on periodic boundary conditions. Different regions of interest, or 'patches', are connected using self energy terms which encode the information of the extended parts of the system. The calculation scheme uses a combination of analytic expressions for the Green's function of infinite pristine systems and an adaptive recursive Green's function technique for the patches. The method allows for an efficient calculation of both local electronic and transport properties, as well as the inclusion of multiple probes in arbitrary geometries embedded in extended samples. We apply the Patched Green's function method to evaluate the local densities of states and transmission properties of graphene systems with two kinds of deviations from the pristine structure: bubbles and perforations with characteristic dimensions of the order of 10-25 nm, i.e. including hundreds of thousands of atoms. The strain field induced by a bubble is treated beyond an effective Dirac model, and we demonstrate the existence of both Friedel-type oscillations arising from the edges of the bubble, as well as pseudo-Landau levels related to the pseudomagnetic field induced by the nonuniform strain. Secondly, we compute the transport properties of a large perforation with atomic positions extracted from a TEM image, and show that current vortices may form near the zigzag segments of the perforation.

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Section: Adaptive Recursion For Device Regionmentioning

confidence: 99%

Patched Green's function techniques for two-dimensional systems: Electronic behavior of bubbles and perforations in graphene

et al. 2015

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“…It has also been adapted to Hall geometries with four terminals [30] and to calculate nonequilibrium densities [31,32]. Furthermore, the RGF algorithm has been formulated to be suitable for parallel computing [33].…”

Section: Introductionmentioning

confidence: 99%

Optimal block-tridiagonalization of matrices for coherent charge transport

Wimmer

Richter

2009

Journal of Computational Physics

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Numerical quantum transport calculations are commonly based on a tight-binding formulation. A wide class of quantum transport algorithms requires the tight-binding Hamiltonian to be in the form of a block-tridiagonal matrix. Here, we develop a matrix reordering algorithm based on graph partitioning techniques that yields the optimal block-tridiagonal form for quantum transport. The reordered Hamiltonian can lead to significant performance gains in transport calculations, and allows to apply conventional two-terminal algorithms to arbitrary complex geometries, including multi-terminal structures. The block-tridiagonalization algorithm can thus be the foundation for a generic quantum transport code, applicable to arbitrary tight-binding systems. We demonstrate the power of this approach by applying the block-tridiagonalization algorithm together with the recursive Green's function algorithm to various examples of mesoscopic transport in two-dimensional electron gases in semiconductors and graphene.

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“…We again reiterate that this procedure is exact; no approximations or truncations have been performed at any stage of the computation. Recursive techniques such as this, which make use of the sparsity of the Hamiltonian matrix, are very widely used in the quantum transport community to compute Green's functions [54][55][56][57][58][59].…”

Section: A Green's Functions and The Local Density Of Statesmentioning

confidence: 99%

Revisiting quasiparticle scattering interference in high-temperature superconductors: The problem of narrow peaks

2017

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We revisit the interpretation of quasiparticle scattering interference in cuprate high-T c superconductors. This phenomenon has been very successful in reconstructing the dispersions of d-wave Bogoliubov excitations, but the successful identification and interpretation of quasiparticle interference (QPI) in scanning tunneling spectroscopy (STS) experiments rely on theoretical results obtained for the case of isolated impurities. We introduce a highly flexible technique to simulate STS measurements by computing the local density of states using real-space Green's functions defined on two-dimensional lattices with as many as 100 000 sites. We focus on the following question: to what extent can the experimental results be reproduced when various forms of distributed disorder are present? We consider randomly distributed pointlike impurities, smooth "Coulombic" disorder, and disorder arising from random on-site energies and superconducting gaps. We find an apparent paradox: the QPI peaks in the Fourier-transformed local density of states appear to be sharper and better defined in experiment than those seen in our simulations. We arrive at a no-go result for smooth-potential disorder since this does not reproduce the QPI peaks associated with large-momentum scattering. An ensemble of pointlike impurities gets closest to experiment, but this goes hand in hand with impurity cores that are not seen in experiment. We also study the effects of possible measurement artifacts (the "fork mechanism"), which turn out to be of relatively minor consequence. It appears that a more microscopic model of the tunneling process needs to be incorporated in order to account for the sharpness of the experimentally obtained QPI peaks.

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Parallel implementation of the recursive Green’s function method

Cited by 29 publications

References 19 publications

Patched Green's function techniques for two-dimensional systems: Electronic behavior of bubbles and perforations in graphene

Patched Green's function techniques for two-dimensional systems: Electronic behavior of bubbles and perforations in graphene

Optimal block-tridiagonalization of matrices for coherent charge transport

Revisiting quasiparticle scattering interference in high-temperature superconductors: The problem of narrow peaks

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