Type II Superconducting Cylindrical Filament in a Non-Uniform Parallel Magnetic Field

Abstract

By means of a two-step unitary transformation, the exact quantum mechanical solution of two-dimensional mesoscopic circuit coupled via inductance is derived. The wavefunction, propagator and expectation value of Hamiltonian are evaluated. The fluctuations of charges and currents are calculated and uncertainty products between charges and their conjugate currents are obtained. We apply our results to the system with special cases of the power source such as the sinusoidal and the sawtooth power source and show that the probability densities oscillate with time due to the power source.

Dependence of the electron-LO-phonon intrasubband scattering rates near a cylindrical cavity on the axial applied magnetic field

“…The dependence of the onset and the period of the oscillations of the scattering integrals on the electron's energies is by and large analytically indeterminate. For example, the onset of the scattering integrals shown in figure 1 is at a lower value of y for a higher value of the magnetic field, in stark contrast to the results obtained previously [26]. Purely from a mathematical point of view, lower values of the scattering rates will be obtained corresponding to which the onset of the oscillations of the scattering integrals is at low values of the off-axial phonon wave number, and vice versa.…”

“…Finally, ω L is the LO-phonon zone-centre frequency, with hω L = 36.6 meV. The mathematical details for the derivations of the scattering rates presented here are very similar to those given in a number of earlier investigations [2,3,26] and are therefore not repeated here. The main results of these investigations are merely quoted here as follows:…”

Surface nucleation of superconductivity near a current-carrying core

“…Recently, there has been a growing interest in the properties of superconducting filamentary systems subjected to a spatially inhomogeneous magnetic field [9][10][11]. The results of a rather simplistic calculation based on the linearized GL equation [9] suggest that there may be possible advantages to be gained from the application of a spatially inhomogeneous magnetic field. The profile of the applied magnetic field may be tailored in such a way as to counteract spatial variations of the superconducting phase, particularly across a thick specimen [10].…”