Aharonov-Bohm magnetic flux

In the presence of a magnetic flux, the boundary condition is changed hy the Aharonov-Bohm effect and the band gap exhibits an oscillation between 0 and 2nylL with period 0q is shown in Fig. 3. 

We next observe that cpM is in units of volt-seconds (V s) or kg m 2/ (A s-2) = J/A. From Eq. (12) it can be seen that A8 and the phase factor, , are dimensionless. Therefore we can make the prediction that if the magnetic flux, (pM, is known and the phase factor, magnetic charge density, gm, can be found by the following relation ... 

First, we note that the standard photodetection is a local measurement of the field variables (intensities). At the same time, the Aharonov-Bohm effect represents a topological measurement referred to the properties of vector potential along some loop. In the usual form, the Aharonov-Bohm effect deals with static or slowly time-varying magnetic fields [101]. The effect consists in the appearance of a persistent current in a metallic loop over which the magnetic flux passes. This current is a periodic function of magnetic flux with the period of flux quantum hc/e. Besides that, certain resistance oscillations in the loop incorporated into an external circuit with the same period can occur. 

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