Abstract
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.
Highlights
Traditional treatment of quantum transport is based on the scattering theory [1]
Non-Hermitian Hamiltonians typically appear in the study of open quantum systems (OQS), where the total Hermitian Hamiltonian of the whole system is projected on the states of its subsystem of interest [2] resulting in a non-Hermitian effective Hamiltonian
Using the developed formalism, we show the possibility of perfect transmission in three-terminal configurations and present simple rules of how to design multi-terminal quantum conductors with perfect transparency
Summary
Traditional treatment of quantum transport is based on the scattering theory [1]. A correspondence between the scattering matrix (S-matrix) and Hamiltonian approaches is established within the framework of Fano–Feshbach formalism [2,3,4]. In our previous works [8,14,15], we have thoroughly studied P T -symmetric two-terminal quantum conductors and have established a direct correspondence between perfect transmission peaks and real eigenvalues of this non-Hermitian auxiliary Hamiltonian. Within this approach, resonance coalescence can be described straightforwardly as a P T -symmetry breaking of the auxiliary Hamiltonian at its exceptional point (EP) [16], where two real eigenvalues coalesce and turn into a complex conjugate pair.
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