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arXiv:0912.0324

Asymmetric coherent transmission for single particle diode and gyroscope

Shengyuan A. Yang, Song, Z., Cai‐Li Sun

Published Dec 2, 2009• 0 citations
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Abstract

We study the single particle scattering process in a coherent multi-site system consisting of a tight-binding ring threaded by an Aharonov-Bohm flux and several attaching leads. The asymmetric behavior of scattering matrix is discovered analytically in the framework of both Bethe Ansatz and Green's function formalism. It is found that, under certain conditions, a three-site electronic system can behave analogous to a perfect semiconductor diode where current flows only in one direction. The general result is also valid for a neutral particle system since the effective magnetic flux may be implemented by a globe rotation. This observation means that the three-site system can serve as an orientation measuring gyroscope due to the approximate linear dependence of the current difference of two output leads on the rotational angular velocity.

DOI
10.48550/arxiv.0912.0324

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As the mechanical counterpart of the Aharonov-Bohm effect and the Aharonov-Cashier effect in a magnetic field, the existence and possibility of observation of a quantum interference effect between the split paths of a coherent particle beam in a uniformly rotating frame have been studied previously. The discussion is now generalized to the case of a reference frame rotating at arbitrarily time-varying angular velocity about a fixed center. The phase difference between the split beams of particles and the resulting interference pattern depend not only upon the speed, but also upon the orientation of the axis of rotation. The conclusion may have, therefore, inferences on gyroscopic applications.
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The scattering of relativistic spin-1/2 neutral particles with a magnetic dipole moment by a long straight charged line and a magnetic flux line at the same position is studied. The scattering cross sections for unpolarized and polarized particles are obtained by solving the Dirac-Pauli equation. The results are in general the same as those for pure Aharonov-Casher scattering (by the charged line alone) as expected. However, in special cases when the incident energy, the line charge density, and the magnetic flux satisfy some relations, the cross section for polarized particles is dramatically changed. Relations between the polarization of incident particles and that of scattered ones are presented, both in the full relativistic case and the nonrelativistic limit. The characteristic difference between the general and special cases lies in the backward direction: in the general cases the incident particles are simply bounced while in the special cases their polarization is turned over simultaneously. For pure Aharonov-Casher scattering there exist cases where the helicities of all scattered particles are reversed. This seems to be remarkable but appears unnoticed previously. Two mathematical approaches are employed to deal with the singularity of the electric and magnetic field and it turns out that the physical results are essentially the same.