Fano resonances in the overlapping regime

Magunov, A. I.; Rotter, I.; Страхова, С. И.

doi:10.1103/physrevb.68.245305

Cited by 47 publications

(44 citation statements)

References 39 publications

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“…Here one of the resonances may appear as some "background" onto which a neighboring resonance is superposed. 28 In Refs. 10 and 26, the phase rigidity ͉͉ 2 with…”

Section: B Scattering Wave Function and Transmissionmentioning

confidence: 99%

Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime

2007

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We study the transmission through different small systems as a function of the coupling strength v to the two attached leads. The leads are identical with only one propagating mode C E in each of them. In addition to the conductance G, we calculate the phase rigidity of the scattering wave function ⌿ C E in the interior of the system. Most interesting results are obtained in the regime of strongly overlapping resonance states where the crossover from staying to traveling modes takes place. The crossover is characterized by collective effects.Here, the conductance is plateaulike enhanced in some energy regions of finite length while corridors with zero transmission ͑total reflection͒ appear in other energy regions. This transmission picture depends only weakly on the spectrum of the closed system. It is caused by the alignment of some resonance states of the system with the propagating modes C E in the leads. The alignment of resonance states takes place stepwise by resonance trapping, i.e., it is accompanied by the decoupling of other resonance states from the continuum of propagating modes. This process is quantitatively described by the phase rigidity of the scattering wave function. Averaged over energy in the considered energy window, ͗G͘ is correlated with 1 − ͗͘. In the regime of strong coupling, only two short-lived resonance states survive each aligned with one of the channel wave functions C E . They may be identified with traveling modes through the system. The remaining M − 2 trapped narrow resonance states are well separated from one another.

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“…Here one of the resonances may appear as some "background" onto which a neighboring resonance is superposed. 28 In Refs. 10 and 26, the phase rigidity ͉͉ 2 with…”

Section: B Scattering Wave Function and Transmissionmentioning

confidence: 99%

Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime

2007

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“…Therefore, we will not consider double poles of the S matrix in the following, but will look at the points and their energies E c where the two eigenvalues z k , z l coalesce. In such a case, the transmission is determined mainly by interferences between the two resonance states k and l. These interferences influence strongly the line shape of resonances [7,15].…”

Section: Effective Hamiltonian and S Marix Theory For Transmis-simentioning

confidence: 99%

“…In [5,6,14,15], the line shape of resonances in the very neighborhood of double poles of the S matrix is studied.…”

Section: Introductionmentioning

confidence: 99%

Influence of branch points in the complex plane on the transmission through double quantum dots

Rotter

Sadreev

2004

Phys. Rev. E

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We consider single-channel transmission through a double quantum dot system consisting of two single dots that are connected by a wire and coupled each to one lead. The system is described in the framework of the S matrix theory by using the effective Hamiltonian of the open quantum system. It consists of the Hamiltonian of the closed system (without attached leads) and a term that accounts for the coupling of the states via the continuum of propagating modes in the leads.This model allows to study the physical meaning of branch points in the complex plane. They are points of coalesced eigenvalues and separate the two scenarios with avoided level crossings and without any crossings in the complex plane. They influence strongly the features of transmission through double quantum dots.

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“…Resonance states with vanishing width ('ghost resonances' (Ladron de Guevara et al, 2003)) may cause, in a natural manner, zeros in the transmission through double quantum dots (and double microwave billiards) when this is required by the unitarity condition (Rotter andSadreev, 2004, 2005b). Furthermore, the line shape of resonances is strongly influenced by interferences between neighboring resonances (Magunov et al, 2003b). It may be fitted even by a complex Fano parameter as suggested by experimental results (Kobayashi et al, 2002).…”

Section: Transmission Through Double Quantum Dotsmentioning

confidence: 91%

Singularities Caused by Coalesced Complex Eigenvalues of an Effective Hamilton Operator

Rotter

Sadreev

2007

Int J Theor Phys

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The S matrix theory with use of the effective Hamiltonian is sketched and applied to the description of the transmission through double quantum dots. The effective Hamilton operator is non-hermitian, its eigenvalues are complex, the eigenfunctions are bi-orthogonal. In this theory, singularities occur at points where two (or more) eigenvalues of the effective Hamiltonian coalesce. These points are physically meaningful: they separate the scenario of avoided level crossings from that without any crossings in the complex plane. They are branch points in the complex plane. Their geometrical features are different from those of the diabolic points.

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Fano resonances in the overlapping regime

Cited by 47 publications

References 39 publications

Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime

Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime

Influence of branch points in the complex plane on the transmission through double quantum dots

Singularities Caused by Coalesced Complex Eigenvalues of an Effective Hamilton Operator

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