Real-space method for highly parallelizable electronic transport calculations

Feldman, Baruch; Seideman, Tamar; Hod, Oded; Kronik, Leeor

doi:10.1103/physrevb.90.035445

Cited by 12 publications

(77 citation statements)

References 67 publications

(108 reference statements)

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“…In particular, Sections 3.2 and 3.3 present two major applications containing Au(111) nanowires from Ref. [1], each of which we compute here in far less CPU time than in Ref. [1], on the same hardware.…”

Section: The Shift-without-invert Partition Algorithmmentioning

confidence: 99%

“…[1], each of which we compute here in far less CPU time than in Ref. [1], on the same hardware. The third major application from Ref.…”

Section: The Shift-without-invert Partition Algorithmmentioning

confidence: 99%

“…Here h is the grid spacing of the real-space lattice and N is typically 10 4 to 10 6 or greater. To correct for the finite volume V , the imaginary absorbing potentials, iΓ, are tuned to absorb outgoing electrons and prevent reflections at the boundaries of the simulation cell [1]. Since H KS is real-symmetric, the presence of iΓ results in a complex-symmetric eigenproblem.…”

Section: Introductionmentioning

confidence: 99%

“…[6,7]) partition the large eigenproblem into parallel subproblems, but must still face the complexity associated with shift-inverse. For our problem, the matrix (2) is very large, and furthermore, the matrix H KS in TRANSEC is never explicitly computed or stored [1,2], even in a standard sparse format; it is instead represented as a matrix-vector product formula. These facts make inversion via ILU factorization infeasible (even if it may be possible to store the sparse H KS explicitly, the cost of factorization can still be prohibitive due to the matrix size).…”

Section: Introductionmentioning

confidence: 99%

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A partitioned shift-without-invert algorithm to improve parallel eigensolution efficiency in real-space electronic transport

Feldman

Zhou

2016

Computer Physics Communications

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We present an eigenspectrum partitioning scheme without inversion for the recently described real-space electronic transport code, TRANSEC. The primary advantage of TRANSEC is its highly parallel algorithm, which enables studying conductance in large systems. The present scheme adds a new source of parallelization, significantly enhancing TRANSEC's parallel scalability, especially for systems with many electrons. In principle, partitioning could enable super-linear parallel speedup, as we demonstrate in calculations within TRANSEC. In practical cases, we report better than five-fold improvement in CPU time and similar improvements in wall time, compared to previously-published large calculations. Importantly, the suggested scheme is relatively simple to implement. It can be useful for general large Hermitian or weakly nonHermitian eigenvalue problems, whenever relatively accurate inversion via direct or iterative linear solvers is impractical.

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Section: The Shift-without-invert Partition Algorithmmentioning

confidence: 99%

“…[1], each of which we compute here in far less CPU time than in Ref. [1], on the same hardware. The third major application from Ref.…”

Section: The Shift-without-invert Partition Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A partitioned shift-without-invert algorithm to improve parallel eigensolution efficiency in real-space electronic transport

Feldman

Zhou

2016

Computer Physics Communications

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“…Nevertheless, the IOBM method still requires the inversion of the Hamiltonian matrix in electrode regions and the computation for solving the generalized eigenvalue problem with very dense matrices. To avoid these inversion-related problems, Feldman et al 29,30 recently proposed a transport calculation method based on Green's function by using the adsorbing boundary condition instead of the self-energy matrices of electrodes. However, the use of an adsorbing boundary condition requires several parameters to be tuned manually to remove spurious reflections at the boundaries; this may restrict its applicability to complicated electrode materials.…”

Section: Introductionmentioning

confidence: 99%

Contour integral method for obtaining the self-energy matrices of electrodes in electron transport calculations

et al. 2018

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We propose an efficient computational method for evaluating the self-energy matrices of electrodes to study ballistic electron transport properties in nanoscale systems. To reduce the high computational cost incurred in large systems, a contour integral eigensolver based on the Sakurai-Sugiura method combined with the shifted biconjugate gradient method is developed to solve exponential-type eigenvalue problem for complex wave vectors. A remarkable feature of the proposed algorithm is that the numerical procedure is very similar to that of conventional band structure calculations. We implement the developed method in the framework of the real-space higher-order finite difference scheme with nonlocal pseudopotentials. Numerical tests for a wide variety of materials validate the robustness, accuracy, and efficiency of the proposed method. As an illustration of the method, we present the electron transport property of the free-standing silicene with the line defect originating from the reversed buckled phases.

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Improvements on non-equilibrium and transport Green function techniques: The next-generation transiesta

Papior

Lorente

Frederiksen

et al. 2017

Computer Physics Communications

326

291

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We present novel methods implemented within the non-equilibrium Green function code (NEGF) transiesta based on density functional theory (DFT). Our flexible, next-generation DFT-NEGF code handles devices with one or multiple electrodes (Ne ≥ 1) with individual chemical potentials and electronic temperatures. We describe its novel methods for electrostatic gating, contour optimizations, and assertion of charge conservation, as well as the newly implemented algorithms for optimized and scalable matrix inversion, performance-critical pivoting, and hybrid parallellization. Additionally, a generic NEGF "post-processing" code (tbtrans/phtrans) for electron and phonon transport is presented with several novelties such as Hamiltonian interpolations, Ne ≥ 1 electrode capability, bond-currents, generalized interface for user-defined tight-binding transport, transmission projection using eigenstates of a projected Hamiltonian, and fast inversion algorithms for large-scale simulations easily exceeding 10 6 atoms on workstation computers. The new features of both codes are demonstrated and bench-marked for relevant test systems. * The transport of charge, magnetic moments and, in general, any sort of excitation is a fascinating fundamental physical problem that has demanded attention for a long time [1]. Today, the interest is enhanced by the technological needs of an industry increasingly based on devices whose detailed atomistic structure matters [2], but the treatment of transport is still a formidable open task. Spurred by the fast developments of the microelectronic industry, the first attempts to understand electronic transport at the atomic scale where based on scattering theory [3]. The electron transmission between two semi-infinite reservoirs was treated in a time-independent fashion solving the scattering matrix connecting the reservoirs. At this stage, transport was described as one-electron scattering by a static contact region and this granted access to many concepts and to devising new experiments [4][5][6]. However, the problem is fundamentally a non-equilibrium one that requires evolving many-body states [7][8][9][10].Density functional theory (DFT) has been one method to address some aspects of this problem. Conceptually, DFT is a mean-field many-body theory of the ground state. As such, it can in principle give exact results for the linear conductance because the linear response is a property of the ground state [11]. Beyond linear conductance, not even ideal DFT works because of the need to describe excited states and dynamics of the system. Such limitations may be mitigated by using time-dependent DFT [12,13], but going beyond the linear regime is highly nontrivial. A main issue of a DFT description stems from the approximations made to compute the ground state. Indeed, it has been recently shown that cases where strong correlations rein, such as the Coulomb blockade regime, the commonly used exchange-and-correlation functionals fail and new ones have to be used [14].Probably the most significant conceptu...

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Real-space method for highly parallelizable electronic transport calculations

Cited by 12 publications

References 67 publications

A partitioned shift-without-invert algorithm to improve parallel eigensolution efficiency in real-space electronic transport

A partitioned shift-without-invert algorithm to improve parallel eigensolution efficiency in real-space electronic transport

Contour integral method for obtaining the self-energy matrices of electrodes in electron transport calculations

Improvements on non-equilibrium and transport Green function techniques: The next-generation transiesta

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