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Modern Physics Letters B

TRANSMISSION PROBABILITY AND PERSISTENT CURRENT IN AN OPEN AHARONOV–BOHM RING

Jian-Duo Lu, Bin Xu, Wei Min Zheng

Published Feb 15, 2012• 2 citations
Publisher

Abstract

We theoretically investigate the transmission probability and the persistent current in an open quantum ring threaded by the magnetic flux. From the numerical results, we find that the two observable quantities both show a periodic characteristic with the increase of the magnetic flux, and they strongly depend on the dimensionless wave vector and the central angle as well as the magnetic flux.

DOI
10.1142/s0217984911500333

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We theoretically investigate the transmission probability and the persistent current in an open quantum ring threaded by the magnetic flux. From the numerical results, we find that the two observable quantities both show a periodic characteristic with the increase of the magnetic flux, and they strongly depend on the dimensionless wave vector and the central angle as well as the magnetic flux.
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 have calculated the persistent spin current of an open ring induced by the Aharonov–Casher phase. For unpolarized electrons there exist no persistent charge currents, but persistent spin currents. We show that, in general, the magnitude of the persistent spin current in a ring depends on the direction of the direct current flow from one reservoir to another. The persistent spin current is modulated by the cosine function of the spin precession angle. The nonadiabatic Aharonov–Casher phase gives anomalous behaviors. The Aharonov–Anandan phase is determined by the solid angle of spin precession. When the nonadiabatic Aharonov–Anandan phase approaches a constant value with the increase of the electric field, the periodic behavior of the spin persistent current occurs in an adiabatic limit. In this limit the periodic behavior of the persistent spin current could be understood by the effective spin-dependent Aharonov–Bohm flux.
The Aharonov-Bohm oscillations in the transmission probability of a one-dimensional mesoscopic ring between two electrodes are considered numerically where a time-periodical flux \ensuremath{\gamma}(t)=\ensuremath{\gamma}+\ensuremath{\lambda} cos\ensuremath{\omega}t is applied. Such a flux simulates a phase-coherent inelastic scattering due to the absorption/emission processes of modulation quanta. An increase of alternating flux amplitude \ensuremath{\lambda} drastically changes the Aharonov-Bohm oscillations of the transmission though the exact period remains ${\mathrm{\ensuremath{\varphi}}}_{0}$=hc/e. A frequency dependence of the transmission has abrupt steps at \ensuremath{\omega}=(E-EF{\mathit{E}}_{\mathit{F}}EF​)/n, caused by the locking of the transmission in the nth channel where EF{\mathit{E}}_{\mathit{F}}EF​ is the Fermi level. Moreover, for transmission of a narrow wave packet the time-periodical flux gives rise to two effects. The first is a fractioning of the input wave packet by the ring in such a way that the output wave function consists of a few separate wave packets. Their number, distance apart, and height essentially depend on the static flux \ensuremath{\gamma}. The second effect is a strong space squeezing of the output wave packet.
A characterization of the two-terminal open-ring Aharonov–Bohm interferometer is made by analyzing the phase space plots in the complex transmission amplitude plane. Two types of plots are considered: type 1 plot uses the magnetic flux as the variable parameter and type 2 plot which uses the electron momentum as the variable parameter. In type 1 plot, the trajectory closes upon itself only when the ratio R of the arm lengths (of the interferometer) is a rational fraction, and the shape and the type of the generated flower-like pattern is sensitive to the electron momentum. For momenta corresponding to discrete eigenstates of the perfect ring (i.e., the ring without the leads), the trajectory passes through the origin a certain fixed number of times before closing upon itself, whereas for arbitrary momenta it never passes through the origin. Although the transmission coefficient is periodic in the flux with the elementary flux quantum as the basic period, the phenomenon of electron transmission is shown not to be so when analyzed via the present technique. The periodicity is seen to spread over several flux units whenever R is a rational fraction whereas there is absolutely no periodicity present when R is an irrational number. In type 2 plot, closed trajectories passing through the origin a number of times are seen for R being a rational fraction. The case R = 1 (i.e., a symmetric ring) with zero flux is rather pathological — it presents a closed loop surrounding the origin. For irrational R values, the trajectories never close.
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.
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.