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. 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 ∼ 0.5 h̄s/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 Vp > T0 the effect of the barrier is to suppress the current amplitude and to shift the crossover temperature from T0 to T ∗ ≃ √VpT0. (Vp is the amplitude of the pinning potential, T0 = h̄vF /L, vF ∼ h̄/ma is the drift velocity of a Wigner crystal ring with lattice spacing a). For very weak pinning, Vp ≪ T0, the influence of the barrier on the persistent current of a Wigner crystal ring is negligibly small. PACS numbers: 73.40.Gk, 7340.Jn Typeset using REVTEX