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Journal of Physics A Mathematical and General

Persistent fluxon current via the Aharonov-Casher effect in one-dimensional mesoscopic rings: continuum model

Jian‐Xin Zhu, Z D Wang, Q. W. Shi

Published Dec 7, 1994• 6 citations
Publisher

Abstract

By extending Lieb and Liniger's (1963) Bose gas analysis to many hard-core bosons confined to a one-dimensional mesoscopic ring in the presence of Aharonov-Casher flux (AC), persistent fluxon currents are investigated for the first time, and are found to be periodic in the AC flux with period Phi 0=hc/e. The interesting mesoscopic parity effects due to evenness or oddness of the particle number N are discussed. More importantly, it is demonstrated exactly that, in the absence of the external AC flux, whether a self-sustained fluxon current exists depends only upon the choice of the boundary condition.

DOI
10.1088/0305-4470/27/23/002

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By extending Lieb and Liniger's (1963) Bose gas analysis to many hard-core bosons confined to a one-dimensional mesoscopic ring in the presence of Aharonov-Casher flux (AC), persistent fluxon currents are investigated for the first time, and are found to be periodic in the AC flux with period Phi 0=hc/e. The interesting mesoscopic parity effects due to evenness or oddness of the particle number N are discussed. More importantly, it is demonstrated exactly that, in the absence of the external AC flux, whether a self-sustained fluxon current exists depends only upon the choice of the boundary condition.
Using a tight-binding model Hamiltonian and applying the Jordan-Wigner transformation, we have investigated the Aharonov-Casher (AC) effect for many neutral hard-core bosons in one-dimensional (1D) mesoscopic rings with the self-induced AC phase included. The total energy and the persistent fluxon current are analytically derived for 1D perfect lattices. More importantly, it is suggested that, in the absence of the external AC flux, the self-sustained AC flux state could be the ground state of a system with weak disorder. The possibility of experimenal observations is briefly discussed.
We perform analytical calculations to study the persistent current I of a q-charged hard-core boson gas in mesoscopic rings enclosing a magnetic flux \ensuremath{\Phi}, and find that this current is periodic in \ensuremath{\Phi} with the period ${\mathrm{\ensuremath{\Phi}}}_{0}$=hc/q. More interestingly, in the presence of a single \ensuremath{\delta}-function impurity, it has been found that there generally exists a spontaneous Aharonov-Bohm flux as long as the current-induced flux is included.
Based upon a tight-binding model Hamiltonian and by applying the Jordan-Wigner transformation, the Aharonov-Bohm (AB) effect for charged hard-core bosons in one-dimensional (1D) mesoscopic rings is investigated for the first time. By introducing a specific unitary transformation, the energy spectrum and the persistent charge current are analytically derived for ID perfect lattices. Similar to electron systems, it has been found that the energy and persistent current are periodic in AB flux with the period Φ0=hc/q. More interestingly, we have exactly shown that, in the absence of the external AB flux, the charge current can be self-sustained via the AB effect, which is in fact the ground state of the system regardless of the number of hard-core bosons being even or odd.
We study the effects of correlations on a one-dimensional ring threaded by a uniform magnetic flux. In order to describe the interaction between particles, we work in the framework of the Hubbard model and the t - and t - - models. We focus on the dilute limit. Our results suggest the possibility that the persistent current has an anomalous periodicity , where p is an integer in the range ( is the number of particles in the ring and is the flux quantum). We find that this result depends neither on disorder nor on the detailed form of the interaction, while there is still on-site infinite repulsion.
We investigate anomalous oscillations due to the Aharonov-Bohm(AB) and Aharonov-Casher(AC) effects of the one-dimensional Hubbard ring with flux in the strong coupling limit. By using the exact diagonalization method and the Shiba transformation, we examine the energies of the ground state and few excited states in the presence of the flux producing the AB or AC effect, where the transformation not only reverses the sign of the interaction U, but also exchanges the role between the AB and AC effects in the model Hamiltonian. We classify the number of oscillation of the ground state as a function of the flux systematically and clarify the close relationship between the AB and AC effects. For example, it is shown that the number of the periods are given by N_L - N_e(N_L - N_↑ + N_↓) for the AB(AC) effect in the very strong attraction, where N_L, N_e, N_↑, and N_↓ are the system size, the number of the total electrons, the number of electrons with up-spin, and the number of electrons with down-spin, respectively, in the condition of N_L > N_e > N_↓ > N_↑. More special case, such as the half-filled band and spin balanced case (N_L = N_e and N_↓ = N_↑ ), we find the periodicity of the system to be 0(2) for the AB(AC) effect in the very strong repulsion. These results show us the nature of interesting phenomena originated by the interplay between the strong correlation and the quantum interference effect in the mesoscopic ring.