Aharonov-Bohm Oscillations in a One-Dimensional Wigner Crystal-Ring

TL;DR

This paper investigates the behavior of persistent currents in a one-dimensional Wigner crystal ring, analyzing how pinning and tunneling affect the current's temperature dependence and quantum coherence.

Contribution

It provides a detailed analysis of how pinning strength influences macroscopic quantum tunneling and persistent currents in a Wigner crystal ring, including the effects of barriers and temperature.

Findings

Persistent current behavior is similar to non-interacting electrons in perfect rings.

Pinning barriers suppress current and alter temperature dependence.

Strong pinning leads to a peak in current at specific temperatures.

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 in a perfect ring 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 --- the reduced barrier height for macroscopic tunneling and loss of quantum coherence --- may result in a sharp peak in the temperature dependence. The character of the macroscopic quantum tunneling of a Wigner crystal ring is dictated by the strength of pinning. At strong pinning the tunneling of a rigid Wigner crystal chain is highly inhomogeneous, and the persistent current has a well-defined peak at $T\sim 0.5\ \hbar s/L$ independent of the barrier height ($s$ is the sound velocity of the Wigner crystal, $L$ is the length of the ring). In the weak pinning regime, the Wigner crystal tunnels through the barrier as a whole and if $V_p>T_0$ the effect of the barrier is to suppress the current amplitude and to shift the crossover temperature from $T_0$ to $T^*\simeq \sqrt{V_{p}T_{0}}$. ($V_{p}$ is the amplitude of the pinning potential, $T_{0} =\hbar v_{F}/L ,\; v_{F}\sim \hbar/ma $ is the drift velocity of a Wigner crystal ring with lattice spacing $a$). For very weak pinning, $V_p\ll T_0$, the influence of the barrier on the persistent current of a Wigner crystal ring is negligibly small.