Electron transport in an open mesoscopic metallic ring

Abstract

We study electron transport in a normal metallic ring modelled by a tight-binding lattice Hamiltonian, coupled to two electron reservoirs. First, Büttiker’s model of incorporating inelastic scattering, and 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 a magnetic flux. We show with this extension that 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 in an analogous way to the four-probe measurement. The local electrochemical potential oscillates in the ring sites because of quantum-interference effects. This predicts that the measured four-point resistance also fluctuates and even can be negative. Then we point out the role of the electronic eigenstates of the closed ring 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.