Aharonov-Bohm effect in one-channel weakly disordered rings
E. P. Nakhmedov, H. Feldmann, R. Oppermann
Abstract
A new diagrammatic method, which is a reformulation of Berezinskii's technique, is constructed to study the density of electronic states ρ(ε,ϕ) of a one-channel weakly disordered ring, threaded by an external magnetic flux. The exact result obtained for the density of states shows an oscillation of ρ(ε,ϕ) with a period of the flux quantum ϕ0= hc/e . As the sample length (or the impurity concentration) is reduced, a transition takes place from the weak localization regime (L >> l) to the ballistic one (L <= l). The analytical expression for the density of states shows the exact dependence of ρ(ε,ϕ) on the ring's circumference and on disorder strength for both regimes.
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