Linear scaling quantum transport methodologies
Fan, Zheyong (Bohai University. School of Mathematics and Physics)
Garcia, José H. (Institut Català de Nanociència i Nanotecnologia)
Cummings, Aron (Institut Català de Nanociència i Nanotecnologia)
Barrios Vargas, José Eduardo (Universidad Nacional Autónoma de México. Departamento de Física y Química Teórica)
Panhans, Michel (Technische Universität Dresden. Center for Advancing Electronics)
Harju, Ari (Varian Medical Systems Finland)
Ortmann, Frank (Institut Català de Nanociència i Nanotecnologia)
Roche, Stephan (Institut Català de Nanociència i Nanotecnologia)

Date:	2021
Abstract:	In recent years, predictive computational modeling has become a cornerstone for the study of fundamental electronic, optical, and thermal properties in complex forms of condensed matter, including Dirac and topological materials. The simulation of quantum transport in realistic models calls for the development of linear scaling, or order-N, numerical methods, which then become enabling tools for guiding experimental research and for supporting the interpretation of measurements. In this review, we describe and compare different order-N computational methods that have been developed during the past twenty years, and which have been used extensively to explore quantum transport phenomena in disordered media. We place particular focus on the zero-frequency electrical conductivities derived within the Kubo-Greenwood​ and Kubo-Streda formalisms, and illustrate the capabilities of these methods to tackle the quasi-ballistic, diffusive, and localization regimes of quantum transport in the noninteracting limit. The fundamental issue of computational cost versus accuracy of various proposed numerical schemes is addressed in depth. We then illustrate the usefulness of these methods with various examples of transport in disordered materials, such as polycrystalline and defected graphene models, 3D metals and Dirac semimetals, carbon nanotubes, and organic semiconductors. Finally, we extend the review to the study of spin dynamics and topological transport, for which efficient approaches for calculating charge, spin, and valley Hall conductivities are described.
Grants:	European Commission 881603 Ministerio de Economía y Competitividad SEV-2017-0706
Note:	Altres ajuts: SR, AWC and JHG acknowledge PRACE and the Barcelona Supercomputing Center (Project No. 2015133194). ICN2 is funded by the CERCA Programme/Generalitat de Catalunya.
Rights:	Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.
Language:	Anglès
Document:	Article ; recerca ; Versió publicada
Subject:	Quantum transport ; 2D materials ; Numerical methods ; Topological materials ; Kernel polynomials method ; Time-dependent Schrödinger equation
Published in:	Physics Reports, Vol. 903 (April 2021) , p. 1-69, ISSN 0370-1573

DOI: 10.1016/j.physrep.2020.12.001

69 p, 4.2 MB

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Research literature > UAB research groups literature > Research Centres and Groups (research output) > Experimental sciences > Catalan Institute of Nanoscience and Nanotechnology (ICN2)
Articles > Research articles
Articles > Published articles