Optimal block-tridiagonalization of matrices for coherent charge transport

Wimmer, Michael; Richter, Klaus

doi:10.1016/j.jcp.2009.08.001

Cited by 59 publications

(59 citation statements)

References 70 publications

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“…12 Moreover, we compare the results to the LandauZener approximation for ballistic systems. The electron mean free path l e is estimated from the disorder strength.…”

Section: A Numerical Methodsmentioning

confidence: 99%

Spin transmission control in helical magnetic fields

2012

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We calculate spin transport in two-dimensional waveguides in the presence of spatially modulated Zeeman-split energy bands. We show that in a regime where the spin evolution is predominantly adiabatic the spin backscattering rate can be tuned via diabatic Landau-Zener transitions between the spin-split bands [Betthausen et al., Science 337, 324 (2012)]. This mechanism is tolerant against spin-independent scattering processes. Completely spinpolarized systems show full spin backscattering, and thus current switching. In partially spin-polarized systems a spatial sequence of Landau-Zener transition points enhances the resistance modulation via reoccupation of backscattered spin-polarized transport modes. We discuss a possible application as a spin transistor.

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“…12 Moreover, we compare the results to the LandauZener approximation for ballistic systems. The electron mean free path l e is estimated from the disorder strength.…”

Section: A Numerical Methodsmentioning

confidence: 99%

Spin transmission control in helical magnetic fields

2012

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“…Alternative approaches have been developed to treat arbitrarily shaped regions with multiple leads [12,13,30]. These so-called knitting algorithms add single sites at a time.…”

Section: Adaptive Recursion For Device Regionmentioning

confidence: 99%

“…Although variants of the method can be used for arbitrary geometries and multiple leads [12][13][14], the method remains limited * mikse@nanotech.dtu.dk to finite-width or periodic systems. Consequently, it cannot describe local and nonperiodic perturbations, or pointlike probes similar to those considered experimentally [15][16][17].…”

Section: Introductionmentioning

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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“…More recent work on the contact-block reduction method 16 divides a generic device into smaller blocks which are pieced together like a jig-saw puzzle. In addition, graph theory has been used to develop a relatively elaborate system permitting the use of LRGF with generic boundary conditions 28 . These results, along with others 21 , suggest the approach we explore in depth in this article, however we argue that the formalism of the "virtual lead" is not necessary.…”

Section: The Outward Wave Methodsmentioning

confidence: 99%

“…To understand how each method contributed to the optimization function, we also plot the size of each matrix that must be inverted for the LRGF and Outward Wave methods for stadia of system size parameter 10 and 40 in Figure 5 as in Wimmer and Richter 28 . The area underneath each function is the same and adds to the total number of orbitals in each system.…”

Section: B Relativistic Stadiums Of Various Sizesmentioning

confidence: 99%

Algorithm for efficient elastic transport calculations for arbitrary device geometries

2011

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With the growth in interest in graphene, controlled nanoscale device geometries with complex form factors are now being studied and characterized. There is a growing need to understand new techniques to handle efficient electronic transport calculations for these systems. We present an algorithm that dramatically reduces the computational time required to find the local density of states and transmission matrix for open systems regardless of their topology or boundary conditions. We argue that the algorithm, which generalizes the recursive Green's Function method by incorporating the reverse Cuthill-McKee algorithm for connected graphs, is ideal for calculating transmission through devices with multiple leads of unknown orientation, and becomes a computational necessity when the input and output leads overlap in real space. This last scenario takes the Landauer-Buttiker formalism to general scattering theory in a computational framework that makes it tractable to perform full-spectrum calculations of the quantum scattering matrix in mesoscopic systems. We demonstrate the efficacy of these approaches on graphene stadiums, a system of recent scientific interest, and contribute to a physical understanding of Fano resonances which appear in these systems.

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Optimal block-tridiagonalization of matrices for coherent charge transport

Cited by 59 publications

References 70 publications

Spin transmission control in helical magnetic fields

Spin transmission control in helical magnetic fields

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

Algorithm for efficient elastic transport calculations for arbitrary device geometries

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