Title:	Effects of the magnetic flux and of the electron momentum on the transmission amplitude in the Aharonov-Bohm interferometer
Authors:	Amaresh Kumar, M.V. Sahoo, Debendranath
Keywords:	Aharonov–Bohm effect transmission amplitude transmittance
Issue Date:	2005
Publisher:	World Scientific
Citation:	International Journal of Modern Physics B, 2005, Vol.19, p3483-3492
Abstract:	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.
Description:	Restricted Access. An open-access version is available at arXiv.org (one of the alternative locations)
URI:	http://hdl.handle.net/2289/2284
ISSN:	0217-9792
Alternative Location:	http://adsabs.harvard.edu/cgi-bin/bib_query?2005IJMPB..19.3483A http://arxiv.org/abs/cond-mat/0506677 http://dx.doi.org/10.1142/S0217979205032218
Copyright:	2005 World Scientific Publishing Company
Appears in Collections:	Research Papers (A&A)

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