Influence of the electron-electron interaction on the Aharonov-Bohm effect

Abstract

It is shown that electron-electron interaction leads, within linear response theory and the first Born approximation, to oscillations of the dc electrical conductivities of weakly disordered rings as a function of the magnetic flux $\phi$ which penetrates the sample. For very low temperatures the period of the oscillations is ${\phi }_0=\frac{h}{e}$ despite the presence of the harmonic $\frac{{\phi }_0}{2}$. The latter is obtained when the magnitude of the relative velocity of two electrons scattered by impurities is conserved. Otherwise the dependence of the conductivities on the flux is more complex. As the temperature grows the oscillations ${\phi }_0$ die out and the harmonic $\frac{{\phi }_0}{2}$ dominates.