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

Details 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

2007-08-14

arxiv.org/abs/0708.1910v2

Physics

Condensed Matter

Other Condensed Matter

Resonance trapping mechanism explained in the captions of Figs. 7 to 11. Recent papers added in the list of references

Scientific paper

10.1103/PhysRevB.76.214302

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 $\xi^E_C$ in each of them. Besides the conductance $G$, we calculate the phase rigidity $\rho$ of the scattering wave function $\Psi^E_C$ 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 plateau-like enhanced in some energy regions of finite length while corridors with zero transmission (total reflection) 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 $\xi^E_C$ 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 $\rho$ of the scattering wave function. Averaged over energy in the considered energy window, $$ is correlated with $1-<\rho>$. In the regime of strong coupling, only two short-lived resonance states survive each aligned with one of the channel wave functions $\xi^E_C$. 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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