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Open AccessArticle

Non-Hermitian Hamiltonians and Quantum Transport in Multi-Terminal Conductors

1
P.N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow 119991, Russia
2
JSC Molecular Electronics Research Institute, Zelenograd, Moscow 124460, Russia
*
Author to whom correspondence should be addressed.
Entropy 2020, 22(4), 459; https://doi.org/10.3390/e22040459
Received: 30 March 2020 / Revised: 13 April 2020 / Accepted: 14 April 2020 / Published: 17 April 2020
(This article belongs to the Special Issue Quantum Dynamics with Non-Hermitian Hamiltonians)
We study the transport properties of multi-terminal Hermitian structures within the non-equilibrium Green’s function formalism in a tight-binding approximation. We show that non-Hermitian Hamiltonians naturally appear in the description of coherent tunneling and are indispensable for the derivation of a general compact expression for the lead-to-lead transmission coefficients of an arbitrary multi-terminal system. This expression can be easily analyzed, and a robust set of conditions for finding zero and unity transmissions (even in the presence of extra electrodes) can be formulated. Using the proposed formalism, a detailed comparison between three- and two-terminal systems is performed, and it is shown, in particular, that transmission at bound states in the continuum does not change with the third electrode insertion. The main conclusions are illustratively exemplified by some three-terminal toy models. For instance, the influence of the tunneling coupling to the gate electrode is discussed for a model of quantum interference transistor. The results of this paper will be of high interest, in particular, within the field of quantum design of molecular electronic devices. View Full-Text
Keywords: non-Hermitian Hamiltonians; open quantum systems; resonances; quantum conductor; quantum interference non-Hermitian Hamiltonians; open quantum systems; resonances; quantum conductor; quantum interference
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MDPI and ACS Style

Shubin, N.M.; Gorbatsevich, A.A.; Krasnikov, G.Y. Non-Hermitian Hamiltonians and Quantum Transport in Multi-Terminal Conductors. Entropy 2020, 22, 459.

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