Oscillations of magnetoresistance in a clean hollow cylinder with fluctuating radius

Abstract

We consider magnetic oscillations of resistivity of a clean hollow cylinder with fluctuating radius $R$, threaded by magnetic flux $\Phi$. We demonstrate, that for very weak fluctuations $\Delta R\ll p_F^{-1}$ the oscillations have a standard period $2{\Phi }_0$ (where ${\Phi }_0=\pi c\hslash /2e$), characteristic for oscillations in a clean system, while for $\Delta R\gg p_F^{-1}$ they become ${\Phi }_0$-periodic, which was expected only for dirty systems with $R\gg l$. The work is motivated by observation of predominantly ${\Phi }_0$-periodic magnetic oscillations in very clean Bismuth wires.