Aharonov-Bohm effect in one-channel weakly disordered rings

Abstract.

A new diagrammatic method, which is a reformulation of Berezinskii's technique, is constructed to study the density of electronic states $p\left( {\varepsilon ,\phi } \right)$ 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 $p\left( {\varepsilon ,\phi } \right)$ with a period of the flux quantum ${\phi _0} = {{hc} \over e}$. As the sample length (or the impurity concentration) is reduced, a transition takes place from the weak localization regime $(L \gg l)$ to the ballistic one $(L \le l)$. The analytical expression for the density of states shows the exact dependence of $p\left( {\varepsilon ,\phi } \right)$ on the ring's circumference and on disorder strength for both regimes.