Aharonov - Bohm - Casher oscillations in strongly correlated electron systems at finite temperature

Abstract

Persistent charge and spin currents due to Aharonov - Bohm and Aharonov - Casher interferences of correlated electrons moving along a mesoscopic ring are discussed at finite temperature. As a function of applied flux the ground-state persistent currents have the shape of a generalized saw-tooth, i.e. they consist of piecewise straight segments. The periods and amplitudes of the oscillations are associated with the properties of the Fermi surface of the elementary excitations (two Dirac seas), namely the group velocities and the matrix of dressed generalized charges (Luttinger parameters). The temperature reduces the amplitudes of oscillation by smearing the Fermi surface in a similar way to that for the de Haas - van Alphen effect in 3D metals. The amplitude of higher harmonics decreases more quickly with T than the fundamental one, changing the saw-tooth to a more sinusoidal form with much smaller amplitude. The controlling parameters are the ratios of the thermal energy to the level spacings in the ring. The results are discussed in the context of the exact Bethe ansatz solutions for the Hubbard chain and the supersymmetric t - J model.