Aharonov-Bohm oscillations in a one-dimensional Wigner crystal ring

We calculate the magnetic moment (''persistent current'') in a strongly correlated electron system - a Wigner crystal - in a one-dimensional ballistic ring, for screened and for long-range Coulomb interactions. 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 noninteracting 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 for screened Coulomb forces has a well-defined peak at T similar to <0.5(h)over bar s/L> independent of the barrier height (s is the sound velocity of the Wigner crystal and 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-* similar or equal to root VpT0. (V-p is the amplitude of the pinning potential, T-0 = <(h) over bar v(F)/L>, v(F) similar to <(h) over bar/ma> is the drift velocity of a Wigner crystal ring with lattice spacing a.) For very weak pinning, V-p much less than T-0, the influence of the barrier on the persistent current of a Wigner crystal ring is negligibly small. We have also shown that unscreened, long-range Coulomb interactions increase the stiffness of the Wigner lattice. This leads to additional suppression of the amplitude of Aharonov-Bohm oscillations, but makes the predicted anomalous temperature dependence of the persistent current in the strong pinning limit even more pronounced. The corresponding temperature of the peak will also be shifted by a factor which depends on the number of particles in the ring. The impact of dissipation on the persistent current of a Wigner crystal ring is also studied.