Analytic Study of Persistent Current in a Two-Channel Disordered Mesoscopic Ring

We present an extensive analytical study of persistent current in a weakly disordered two-chain cylindrical ring threaded by an Aharonov-Bohm flux $0 < \phi <\phi_0/2$ (with $\phi_0$ the flux quantum) and described by the Anderson model. The effect of the disorder reveals a strong reduction of the persistent current for flux values near $\phi_0/4$. In conjunction with the pure system (zeroth order) current profile averaged over numbers of electrons and earlier results for the effect of disorder in one-dimensional rings, our two-channel results provide a simple interpretation of salient features of numerical results of Bouchiat and Montambaux (BM) for persistent current in an assembly of many-channel disordered rings. Single-channel (one-dimensional) effects are responsible for the dip in the persistent obtained by BM near $\phi=0$ and the corresponding peak near $\phi_0/2$, while the effect of disorder in independent channel pairs accounts for abrupt decreases of current superimposed to a continuous linear decay as the flux value $\phi_0/4$ is approached from above and from below, respectively. The persistent current in the two-channel ring involves a free particle current averaged over electron numbers of periodicity $\phi_0/2$, and a dominant disorder effect which has periodicity $\phi_0$.