Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 55, Issue 27, Pages -Publisher
IOP Publishing Ltd
DOI: 10.1088/1751-8121/ac7119
Keywords
quantum transport; many-body correlation; non-equilibrium Green's function
Categories
Funding
- Israel Science Foundation [2064/19]
- National Science Foundation-US-Israel Binational Science Foundation [735/18]
- Academy of Finland via the Centre of Excellence program [336810]
- Finnish Cultural Foundation via PoDoCo program [00210085]
- Academy of Finland [308697, 321540, 345007]
- Academy of Finland (AKA) [321540, 308697, 321540, 308697] Funding Source: Academy of Finland (AKA)
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The non-equilibrium Green's function (NEGF) formalism is one of the most versatile theoretical approaches to studying time-dependent correlated quantum transport in nano-systems, capable of treating inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom.
We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems: the non-equilibrium Green's function (NEGF) formalism. Within this formalism, one can treat, on the same footing, inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom. After a historical overview on the theory of transport in quantum systems, we present a modern introduction of the NEGF approach to quantum transport. We discuss the inclusion of inter-particle interactions using diagrammatic techniques, and the use of the so-called embedding and inbedding techniques which take the bath couplings into account non-perturbatively. In various limits, such as the non-interacting limit and the steady-state limit, we then show how the NEGF formalism elegantly reduces to well-known formulae in quantum transport as special cases. We then discuss non-equilibrium transport in general, for both particle and energy currents. Under the presence of a time-dependent drive-encompassing pump-probe scenarios as well as driven quantum systems-we discuss the transient as well as asymptotic behavior, and also how to use NEGF to infer information on the out-of-equilibrium system. As illustrative examples, we consider model systems general enough to pave the way to realistic systems. These examples encompass one- and two-dimensional electronic systems, systems with electron-phonon couplings, topological superconductors, and optically responsive molecular junctions where electron-photon couplings are relevant.
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