Persistent Current of a One-Dimensional Wigner Crystal-Ring

Abstract

We calculate the magnetic moment (`persistent current') in a strongly correlated electron system --- a Wigner crystal --- in a one-dimensional ballistic ring. The flux- and temperature dependence of the persistent current is shown to be essentially the same as for a system of non-interacting electrons. In contrast, by incorporating into the ring geometry a tunnel barrier, that pins the Wigner crystal, the current is suppressed and its temperature dependence is drastically changed. The competition between two temperature effects --- a reduced barrier height for macroscopic tunneling and a loss of quantum coherence --- results in a sharp peak in the temperature dependence, which for a rigid Wigner crystal appears at $T\sim 0.5\ \hbar s/L$, ($s$ is the sound velocity of the Wigner crystal, $L$ is the length of the ring).