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Journal of the Physical Society of Japan

Persistent Current via Aharonov-Bohm Effect for Charged Hard-Core Bosons in One-Dimensional Mesoscopic Rings

Jian‐Xin Zhu, Z. D. Wang

Published Feb 15, 1995• 3 citations
Publisher

Abstract

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.

DOI
10.1143/jpsj.64.335

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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.
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.
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.
Fixed-number-of-electron mesoscopic or macromolecular conducting ring is shown to support persistent currents due to Aharonov-Bohm flux, and the "spontaneous" persistent currents without the flux when structural transformation in the ring is blocked by strong coupling to the externally azimuthal-symmetric environment. In the free-standing macromolecular ring, symmetry breaking removes the azimuthal periodicity which however is further restored at the increasing field. Three-site ring with one or three electrons represent an interesting quantum system which can serve as a qubit (quantum bit of information) and a qugate (quantum logical gate). © 2005 by World Scientific Publishing Co. Pte. Ltd.