Coalescence of resonances in dissipationless resonant tunneling structures and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si23.gif" display="inline" overflow="scroll"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetry breaking

Горбацевич, А. А.; Shubin, N. M.

doi:10.1016/j.aop.2016.12.019

Cited by 17 publications

(28 citation statements)

References 55 publications

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“…[12][13][14] Interaction of resonances can result in their coalescence (collapse of resonances 12,15 ) that was described for semiconductor heterostructures with two resonances 12,16 and for tunneling quantum dots with three resonances. 17,18 Collapse of eigenmodes was also observed in semiconductor cavities with Rabi splitting, 19 classical electrical circuits, 20,21 in quantum tunneling structures 22,23 etc. However coalescence of resonances can not be described in the terms of the scattering matrix poles behavior.…”

Section: Introductionmentioning

confidence: 92%

“…Coalescence of perfect transmission maximums was shown Ref. 18,31 to occur at the EP of the non-Hermitian auxiliary Hamiltonian. Here we focus on the coalescence of transmission zeros (antiresonances) and show that it can be related to an EP of some additional non-Hermitian Hamiltonian as well.…”

Section: Engineering Fano Resonances: Coalescence Of Resonances Anmentioning

confidence: 97%

“…However, if one neglects the energy dependence of self-energy, then Q and P can be cosidered as polynomials. 18 In spatially symmetric structure non-Hermitian auxiliary Hamiltonian (20) becomes PT -symmetric and possesses real eigenvalues. According to Eq.…”

Section: A Effective and Auxiliary Hamiltonians And Exact Location Omentioning

confidence: 99%

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Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models

Горбацевич

Shubin

2017

Phys. Rev. B

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We study transport properties of an arbitrary two terminal Hermitian system within a tightbinding approximation and derive the expression for the transparency in the form, which enables one to determine exact energies of perfect (unity) transmittance, zero transmittance (Fano resonance) and bound state in the continuum (BIC). These energies correspond to the real roots of two energy-dependent functions that are obtained from two non-Hermitian Hamiltonians: the Feshbach's effective Hamiltonian and the auxiliary Hamiltonian, which can be easily deduced from the effective one. BICs and scattering states are deeply connected to each other. We show that transformation of a scattering state into a BIC can be formally described as a "phase transition" with divergent generalized response function. Design rules for quantum conductors and waveguides are presented, which determine structures exhibiting coalescence of both resonances and antiresonances resulting in the formation of almost rectangular transparency and reflection windows. The results can find applications in construction of molecular conductors, broad band filters, quantum heat engines and waveguides with controllable BIC formation.

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Section: Introductionmentioning

confidence: 92%

Section: Engineering Fano Resonances: Coalescence Of Resonances Anmentioning

confidence: 97%

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Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models

Горбацевич

Shubin

2017

Phys. Rev. B

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“…If perfect (unity-valued) resonances become wider and closer to each other, they can coalesce, resulting in a single transmission peak with amplitude smaller than unity [7]. This phenomenon cannot be detected from the analysis of the S-matrix poles alone [8]. In complex systems, where destructive quantum interference (DQI) is possible, much more complicated interference phenomena are expected, so the traditional S-matrix (or effective Hamiltonian) point of view cannot handle all the variety of possible interference effects in quantum transport.…”

Section: Introductionmentioning

confidence: 99%

“…This is impossible for effective Hamiltonian as its eigenvalues (S-matrix poles) are located in the lower half of a complex energy plane. 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.…”

Section: Introductionmentioning

confidence: 99%

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

Shubin

Горбацевич

Krasnikov

2020

Entropy

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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.

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Covert Scattering Control in Metamaterials with Non‐Locally Encoded Hidden Symmetry

Sol,

Röntgen,

del Hougne

2023

Advanced Materials

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Symmetries and tunability are of fundamental importance in wave scattering control, but symmetries are often obvious upon visual inspection which constitutes a significant vulnerability of metamaterial wave devices to reverse‐engineering risks. Here, it is theoretically and experimentally shown that a symmetry in the reduced basis of the “primary meta‐atoms” that are directly connected to the outside world is sufficient; meanwhile, a suitable topology of non‐local interactions between them, mediated by the internal “secondary” meta‐atoms, can hide the symmetry from sight in the canonical basis. Covert symmetry‐based scattering control in a cable‐network metamaterial featuring a hidden parity () symmetry in combination with hidden‐‐symmetry‐preserving and hidden‐‐symmetry‐breaking tuning mechanisms is experimentally demonstrated. Physical‐layer security in wired communications is achieved, using the domain‐wise hidden ‐symmetry as shared secret between the sender and the legitimate receiver. Within the approximation of negligible absorption, the first tuning of a complex scattering metamaterial without mirror symmetry to feature exceptional points (EPs) of ‐symmetric reflectionless states, as well as quasi‐bound states in the continuum, is reported. These results are reproduced in metamaterials involving non‐reciprocal interactions between meta‐atoms, including the first observation of reflectionless EPs in a non‐reciprocal system.This article is protected by copyright. All rights reserved

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Coalescence of resonances in dissipationless resonant tunneling structures and PT-symmetry breaking

Cited by 17 publications

References 55 publications

Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models

Unified theory of resonances and bound states in the continuum in Hermitian tight-binding models

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

Covert Scattering Control in Metamaterials with Non‐Locally Encoded Hidden Symmetry

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