Aharonov-Bohm Oscillations in 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 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 $T\sim 0.5\hslash s/L$ 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 $T^{\ast }\simeq \sqrt{V_p{T}_0}$. ($V_p$ is the amplitude of the pinning potential, $T_0=\hslash v_F/L,v_F\sim \hslash /ma$ 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.

30 pages, RevTeX, 2 figures available on request

References in corpus (6)

• Wigner Crystal in One Dimension
• Wigner Molecules in Nanostructures
• Suppression of Persistent Currents in 1-D Disordered Rings by Coulomb Interaction
• Scaling theory of the Mott-Hubbard metal-insulator transition in one dimension
• A Simple Formula for the Persistent Current in Disordered 1D Rings: Parity and Interaction Effects
• Rigorous upper bound for the persistent current in systems with toroidal geometry

Cited by in corpus (10)

• Comment on "Space-Time Crystals of Trapped Ions": And Yet it Moves Not !
• Charge and Spin Effects in Mesoscopic Josephson Junctions
• Influence of spin on the persistent current of strongly interacting electrons
• Half-filled Hubbard ring with alternating site potentials in a magnetic field
• Coulomb Drag between One-Dimensional Wigner Crystal Rings
• Persistent currents in two dimensions: New regimes induced by the interplay between electronic correlations and disorder
• Effect of a lattice upon an interacting system of electrons in two dimensions: Breakdown of scaling and decay of persistent currents
• Ordering effect of Coulomb interaction in ballistic double-ring systems
• Coulomb correlations and coherent charge tunneling in mesoscopic coupled rings
• Persistent current in a one-dimensional ring of fractionally charged "exclusons''