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Journal of Shanxi Normal University

Persistent Current in the Contacted and Doubled Aharonov-Bohm Rings Coupled to Extent Leads

Luo Guo-zhong

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

In this paper,we studied the problem of persistent current and transmission of two contacted Aharonov-Bohm Rings coupled to extent leads,and give the analytical solution.The conditions of observing persistent current,zero and perfect transmission are discussed,and the Fano resonance is studied.

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Relativistic Persistent Currents in Ideal Aharonov-Bohm Rings and Cylinders

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Abstract In this report we revisit the results obtained in [1, 2] where the relativistic Aharonov-Bohm was studied for the first time. The method is based on the exact solutions of the complete (1+3)-dimensional Dirac equation of fermions moving in ideal Aharonov-Bohm (AB) rings and cylinders which are used for deriving the exact expressions of the relativistic partial currents. It is shown that these currents can be related to the derivative of the fermion energy with respect to the flux parameter, just as in the non-relativistic case. However, a new and remarkable relativistic effect is the saturation of the partial currents for high values of the total angular momentum. Based on this property, the total relativistic persistent currents atT= 0 is evaluated for rings and cylinders obtaining approximative simple closed formulas. Notice that this report brings together the texts of Refs. [1, 2] with some improvements and unitary notations.

arXiv:1606.08372•Annals of West University of Timisoara - Physics•Dec 1, 2016•0 citations
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.
The fractional Aharonov-Bohm oscillation (FABO) of narrow quantum rings with two electrons has been studied and has been explained in an analytical way, the evolution of the period and amplitudes against the magnetic field can be exactly described. Furthermore, the dipole transition of the ground state was found to have essentially two frequencies, their difference appears as an oscillation matching the oscillation of the persistent current exactly. A number of equalities relating the observables and dynamical parameters have been found.
The exact solutions of the complete Dirac equation for fermions moving in ideal Aharonov–Bohm rings are used for deriving the exact expressions of the relativistic partial currents. It is shown that as in the nonrelativistic case, these currents can be related to the derivative of the fermion energy with respect to the flux parameter. A specific relativistic effect is the saturation of the partial currents for high values of the total angular momentum. Based on this property, the total relativistic persistent current at T = 0 is evaluated giving its analytical expression and showing how this depends on the ring parameters.
Abstract We study the persistent current in a chain of two coupled quantum rings threaded by an Aharonov-Bohm flux in the presence of electron-phonon and Rashba spin-orbit interactions. In the framework of the Holstein-Hubbard model, the equations for ground state energy, persistent current and Drude weight were derived. Obtaining of the expression for the ground state energy allowed us to obtain the persistent current by a conventional way (differentiating). The influence of the magnetic flux and the Rashba spin-orbit interaction on the ground state energy, persistent current and Drude weight was studied numerically.
Abstract In this report we revisit the results obtained in [1, 2] where the relativistic Aharonov-Bohm was studied for the first time. The method is based on the exact solutions of the complete (1+3)-dimensional Dirac equation of fermions moving in ideal Aharonov-Bohm (AB) rings and cylinders which are used for deriving the exact expressions of the relativistic partial currents. It is shown that these currents can be related to the derivative of the fermion energy with respect to the flux parameter, just as in the non-relativistic case. However, a new and remarkable relativistic effect is the saturation of the partial currents for high values of the total angular momentum. Based on this property, the total relativistic persistent currents atT= 0 is evaluated for rings and cylinders obtaining approximative simple closed formulas. Notice that this report brings together the texts of Refs. [1, 2] with some improvements and unitary notations.