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

Santos, T. Periera dos; Lima, Leandro R. F.; Lewenkopf, Caio

doi:10.1016/j.jcp.2019.05.034

Cited by 13 publications

(5 citation statements)

References 50 publications

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“…This approach is at the root of the numerical package t-Kwant, 28 which extends to the time domain the quantum transport package Kwant. [88][89][90] To date, t-Kwant has been used for calculating time resolved particle density and particle current in various systems. 29,30,32,33,91,92 The case of particle current noise has also been dealt with in Ref.…”

Section: Methodsmentioning

confidence: 99%

Simulating time-dependent thermoelectric transport in quantum systems

Slimane,

Reck,

Fleury

2019

Preprint

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We put forward a gauge-invariant theoretical framework for studying time-resolved thermoelectric transport in an arbitrary multiterminal electronic quantum system described by a non-interacting tight-binding model. The system is driven out of equilibrium by an external time-dependent electromagnetic field (switched on at time t0) and possibly by static temperature or electrochemical potential biases applied (from the remote past) between the electronic reservoirs. Numerical simulations are conducted by extending to energy transport the wave-function approach developed by Gaury et al. and implemented in the t-Kwant library. We provide a module that allows us to compute the time-resolved heat currents and powers in addition to the (already implemented) charge currents, and thus to simulate dynamical thermoelectric transport through realistic devices, when electron-electron and electron-phonon interactions can be neglected. We apply our method to the non-interacting Resonant Level Model and verify that we recover the results reported in the literature for the time-resolved heat currents in the expected limits. Finally, we showcase the versatility of the library by simulating dynamical thermal transport in a Quantum Point Contact subjected to voltage pulses.

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Section: Methodsmentioning

confidence: 99%

Simulating time-dependent thermoelectric transport in quantum systems

Slimane,

Reck,

Fleury

2019

Preprint

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“…Then the scaling of the computational time goes as aLW + bLW 2 . Consequently, for fixed W, the divideand-conquer algorithm is linear in L, which is on par with the other recursive methods [16][17][18]. On the other hand, if L W then the computational time goes as aLW + bL 2 W, which is linear in W. Figure 4(a) presents the computational time for systems shown in the inset with W L (red squares) and L W (blue circles).…”

Section: Performance Of the Divide-and-conquer Algorithmmentioning

confidence: 96%

“…The transmission function depends strongly on the presence of impurities and defects, the geometry, and the lattice of the systems. Realistic systems consist of a large number of sites, therefore computational efficiency is an essential part of the recursive methods [16,17]. The transfer matrix can be found by multiplying transfer matrices of slices of the system.…”

Section: Introductionmentioning

confidence: 99%

A divide-and-conquer method to improve performance in quantum transport calculations: conductance in rotated graphene nanoribbons side-contact junctions

Rodríguez¹,

García²

2022

Electron. Struct.

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We propose a divide-and-conquer algorithm to find recursively the Scattering matrix of general tight-binding structures. The Scattering matrix allows a direct calculation of transport properties in mesoscopic systems by using the Landauer formula. The method is exact, and by analyzing the performance of the algorithm in square, triangular and honeycomb lattices, we show a significant improvement in comparison to other state-of-the-art recursive and non-recursive methods. We utilize this algorithm to compute the conductance of a rotated graphene nanoribbon side-contact junction, revealing that for electrons with energies smaller than -2.7eV the transmission function depends negligibly on the angle of the junction, whereas for electrons with energies greater than -2.7eV, there exists a set of angles for the system that increase its conductance independently of the energy of the particles.

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“…Santos et al used a graphene Hall bar to introduce a novel self-contained description of the wave-function matching method to calculate electronic quantum transport properties of nanostructures using the Landauer-Büttiker approach [245]. The method is based on partitioning the system-to-besolved into a central conductor and an asymptotic region for the leads.…”

Section: D Materialsmentioning

confidence: 99%

Computational perspective on recent advances in quantum electronics: from electron quantum optics to nanoelectronic devices and systems

Weinbub

Kosik

2022

J. Phys.: Condens. Matter

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Quantum electronics has significantly evolved over the last decades. Where initially the clear focus was on light-matter interactions, nowadays approaches based on the electron's wave nature have solidified themselves as additional focus areas. This development is largely driven by continuous advances in electron quantum optics, electron based quantum information processing, electronic materials, and nanoelectronic devices and systems. The pace of research in all of these areas is astonishing and is accompanied by substantial theoretical and experimental advancements. What is particularly exciting is the fact that the computational methods, together with broadly available large-scale computing resources, have matured to such a degree so as to be essential enabling technologies themselves. These methods allow to predict, analyze, and design not only individual physical processes but also entire devices and systems, which would otherwise be very challenging or sometimes even out of reach with conventional experimental capabilities. This review is thus a testament to the increasingly towering importance of computational methods for advancing the expanding field of quantum electronics. To that end, computational aspects of a representative selection of recent research in quantum electronics are highlighted where a major focus is on the electron's wave nature. By categorizing the research into concrete technological applications, researchers and engineers will be able to use this review as a source for inspiration regarding problem-specific computational methods.

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

Cited by 13 publications

References 50 publications

Simulating time-dependent thermoelectric transport in quantum systems

Simulating time-dependent thermoelectric transport in quantum systems

A divide-and-conquer method to improve performance in quantum transport calculations: conductance in rotated graphene nanoribbons side-contact junctions

Computational perspective on recent advances in quantum electronics: from electron quantum optics to nanoelectronic devices and systems

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