Application of Intrinsic Quantized Flux of Electrons and Holes in Josephson Junctions

Abstract

The aim of this study is to investigate the influence of spin degrees of freedom on the flux quantization in a 2D Josephson junction. One of the most important properties of the Josephson structures is the total quantum flux which can be related to the phase difference across the junction. For example the sign of the phase difference controls the direction of the Josephson current while the magnitude of the phase difference affect the critical current itself. So far in literature to calculate the total quantum flux in the Josephson structures only the flux of the external magnetic field (and hence the external vector potential) has been considered but the intrinsic quantum flux of correlated electrons and holes have not been taken into account. We have recently calculated the intrinsic quantized magnetic flux of electrons and holes. We showed that depending on the spin orientations, the spin contribution to the quantized intrinsic flux of a correlated electron is equal to (Φint = ± g * Φ 02 ). Here g * is the effective Landé g-factor and Φ0 is the unit of flux (fluxoid). In the present study we calculate the above mentioned phase differences across the junction considering the intrinsic quantum flux of electrons and holes. For electrons the additional flux contribution will be: ∆Φint = ± g * e Φ 0 2 and for holes, the related contribution will be:2 . We show that, for both charge carriers, the effective Landé g-factors (g * e , g * h ), take only even integer values such as (0, 2, 4, . . .). The present calculations can be easily extended to the intrinsic Josephson junctions as well. We found that flux contribution to the total flux due to spin is very important and it is in fact ±Φ0/2 depending on the spin up and down cases or the ground state.

Calculation of the Spinning Speed of a Free Electron

“…When an electron is placed in an external magnetic field B, during the cyclotron period T c it completes one turn around the cyclotron orbit, but it spins ( s ω ) times about itself ( Figure 1) [13]. We will see that ( s c ω ω  ).…”

“…Recently we have calculated the magnetic field inside a free electron due to spinning motion [1] and showed that it is about 8.3 × 10 13 T. This field is about 8.3 × 10 11 times bigger than the highest magnetic field obtained in today's laboratories [2] [3] and 10 3 times bigger than that in neutron stars (magnetars) [4] [5]. In that calculations [1], which are based on the current loop model, the intrinsic magnetic flux associated with its spinning motion of the electron which is calculated either by a semiclassical methode or by a full quantum mechanical solution of Dirac equation [6] [7] [8] gives the same result: ( ) 2 Journal of Modern Physics to that spherical charge distribution.…”