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  Effective 1D Time-Dependent Schrödinger Equations for 3D Geometrically Correlated Systems

Pandey, D., Oriols, X., & Albareda Piquer, G. (2020). Effective 1D Time-Dependent Schrödinger Equations for 3D Geometrically Correlated Systems. Materials, 13(13): 3033. doi:10.3390/ma13133033.

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Item Permalink: https://hdl.handle.net/21.11116/0000-0006-DCA0-D Version Permalink: https://hdl.handle.net/21.11116/0000-000B-BBAD-0
Genre: Journal Article

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materials-13-03033-v2.pdf (Publisher version), 806KB
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2020
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© by the authors. Licensee MDPI, Basel, Switzerland.
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https://dx.doi.org/10.3390/ma13133033 (Publisher version)
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 Creators:
Pandey, D.1, Author
Oriols, X.1, Author
Albareda Piquer, G.2, 3, Author           
Affiliations:
1Departament d’Enginyeria Electrònica, Universitat Autònoma de Barcelona, ou_persistent22              
2Theory Group, Theory Department, Max Planck Institute for the Structure and Dynamics of Matter, Max Planck Society, ou_2266715              
3Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, ou_persistent22              

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Free keywords: nanojunction; constriction; quantum electron transport; quantum confinement; dimensionalityreduction; stochastic Schrödinger equations; geometric correlations
 Abstract: The so-called Born–Huang ansatz is a fundamental tool in the context of ab-initio molecular dynamics, viz., it allows effectively separating fast and slow degrees of freedom and thus treating electrons and nuclei with different mathematical footings. Here, we consider the use of a Born–Huang-like expansion of the three-dimensional time-dependent Schrödinger equation to separate transport and confinement degrees of freedom in electron transport problems that involve geometrical constrictions. The resulting scheme consists of an eigenstate problem for the confinement degrees of freedom (in the transverse direction) whose solution constitutes the input for the propagation of a set of coupled one-dimensional equations of motion for the transport degree of freedom (in the longitudinal direction). This technique achieves quantitative accuracy using an order less computational resources than the full dimensional simulation for a typical two-dimensional geometrical constriction and upto three orders for three-dimensional constriction.

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Language(s): eng - English
 Dates: 2020-05-102020-07-012020-07-01
 Publication Status: Published online
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.3390/ma13133033
 Degree: -

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Project name : -
Grant ID : 785219
Funding program : Horizon 2020 (H2020)
Funding organization : European Commission (EC)
Project name : -
Grant ID : 765426
Funding program : Horizon 2020 (H2020)
Funding organization : European Commission (EC)
Project name : -
Grant ID : 752822
Funding program : Horizon 2020 (H2020)
Funding organization : European Commission (EC)
Project name : We acknowledge financial support from Spain’s Ministerio de Ciencia, Innovación y Universidades under Grant No. RTI2018-097876-B-C21 (MCIU/AEI/FEDER, UE), the European Union’s Horizon 2020 research and innovation program under Grant Agreement No. Graphene Core2 785219 and under the Marie Sklodowska-Curie Grant Agreement No. 765426 (TeraApps), and the Generalitat de Catalunya under Grant No. 001-P-001644 (QUANTUM CAT). G.A. also acknowledges financial support from the European Unions Horizon 2020 research and innovation program under the Marie Skodowska-Curie Grant Agreement No. 752822, the Spanish Ministerio de Economa y Competitividad (Project No. CTQ2016-76423-P), and the Generalitat de Catalunya (Project No. 2017 SGR 348).
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Title: Materials
  Abbreviation : Materials
Source Genre: Journal
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Publ. Info: Basel : MDPI
Pages: - Volume / Issue: 13 (13) Sequence Number: 3033 Start / End Page: - Identifier: ISSN: 1996-1944
CoNE: https://pure.mpg.de/cone/journals/resource/1996-1944