Linear scaling quantum transport methodologies
| Autor: | Ari Harju, Aron W. Cummings, Zheyong Fan, J.E. Barrios-Vargas, Jose H. Garcia, Frank Ortmann, Michel Panhans, Stephan Roche |
|---|---|
| Přispěvatelé: | National Natural Science Foundation of China, Center for Science (Finland), European Commission, Ministerio de Economía y Competitividad (España), Generalitat de Catalunya |
| Rok vydání: | 2021 |
| Předmět: |
Dirac (software)
FOS: Physical sciences General Physics and Astronomy 01 natural sciences Schrödinger equation law.invention symbols.namesake law Mesoscale and Nanoscale Physics (cond-mat.mes-hall) 0103 physical sciences Kernel polynomials method Linear scale Time-dependent Schrödinger equation Limit (mathematics) Statistical physics 010306 general physics Spin-½ Physics Condensed Matter - Materials Science Condensed Matter - Mesoscale and Nanoscale Physics 010308 nuclear & particles physics Graphene Numerical analysis Topological materials Materials Science (cond-mat.mtrl-sci) Charge (physics) Disordered Systems and Neural Networks (cond-mat.dis-nn) Condensed Matter - Disordered Systems and Neural Networks 2D materials ddc Quantum transport symbols Numerical methods |
| Zdroj: | Physics Reports Dipòsit Digital de Documents de la UAB Universitat Autònoma de Barcelona |
| ISSN: | 0370-1573 |
| DOI: | 10.1016/j.physrep.2020.12.001 |
| Popis: | 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 materials 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. 54 pages, 31 figures, Invited Review of Physics Reports |
| Databáze: | OpenAIRE |
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