Electron transport in an open mesoscopic metallic ring

We study electron transport in a normal-metal ring modeled by the tight binding lattice Hamiltonian, coupled to two electron reservoirs. First, Buttiker's model of incorporating inelastic scattering, hence decoherence and dissipation, has been extended by connecting each site of the open ring to one-dimensional leads for uniform dephasing in the ring threaded by magnetic flux. We show with this extension conductance remains symmetric under flux reversal, and Aharonov-Bohm oscillations with changing magnetic flux reduce to zero as a function of the decoherence parameter, thus indicating dephasing in the ring. This extension enables us to find local chemical potential profiles of the ring sites with changing magnetic flux and the decoherence parameter analogously to the four probe measurement. The local electrochemical potential oscillates in the ring sites because of quantum-interference effects. It predicts that measured four-point resistance also fluctuates and even can be negative. Then we point out the role of the closed ring's electronic eigenstates in the persistent current around Fano antiresonances of an asymmetric open ring for both ideal leads and tunnel barriers. Determining the real eigenvalues of the non-Hermitian effective Hamiltonian of the ring, we show that there exist discrete bound states in the continuum of scattering states for the asymmetric ring even in the absence of magnetic flux. Our approach involves quantum Langevin equations and non-equilibrium Green's functions.Comment: 19 pages, 6 figure

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

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 $1-$. 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.Comment: Resonance trapping mechanism explained in the captions of Figs. 7 to 11. Recent papers added in the list of reference