Effects of an impurity on the dissipation in a partially coherent flux-driven ring

We have studied a mesoscopic ring threaded by a magnetic flux that increase s linearly with time. The ring is partially coherent, such that conduction electrons in the ring will encounter incoherent scatterings. In addition, t he electrons encounter elastic scatterings due to the presence of an impuri ty in the ring. We have adopted a S-matrix model, as proposed by Buttiker M . Buttiker, Phys. Rev. B 32 (1985) 1846; M. Buttiker, Phys. Rev. B 33 (1986 ) 3020], for the incoherent scatterings in this time-dependent situation. T his allows us to treat the incoherent scatterings, the elastic scatterings and the coherent inelastic processes on the same footing. We have solved th e problem exactly. Our results demonstrate that, in the case of a weak impu rity, the lower the energies of the electrons that emanate out of incoheren t scatterings, the greater will be their net contribution to the de compone nt I-dc of the induced current. In the case of a strong impurity, however, I-dc alternates between regions of zero and nonzero values as the chemical potential mu increases. The peak value of I-dc in the nonzero region increa ses with mu. We find that these regions of zero, and nonzero, I-dc correspo nd closely with the gaps, and the bands, respectively, of a one-dimensional energy band. All these characteristics arise from the fact that the electr ons traversing the ring have their energies shifted gradually until their e nergies fall upon a forbidden region, where they suffer total reflection. T his total reflection at the forbidden region does not occur in a ring that has a constant flux. Rather, it results from the nonadiabatic effect of the changing flux. The evolution of the nonadiabatic effects in the intermedia te impurity regime has also been investigated. (C) 2000 Elsevier Science Lt d. All rights reserved.