Fluxon Dynamics In Couple Long Josephson Junction Based on Two-Gap Superconductors Like MgB2 And Iron-Prictides

Abstract

In the present work, the fluxon dynamics in long Josephson junction based on two-gap superconductors like MgB and iron-pnictides has been studied. The procedure has been started by establishing the microscopic BCS Hamiltonian of the junction system in terms of fermionic field operators. In order to enter in the long route of path integral formalism, the Hamiltonian has been introduced into the quantum mechanical partition function through the definition of Lagrangian density and then action functional. Some important steps such as Hubbard-Stratonovich transformation for bosonization, Nambu representation, reciprocal space transformation, saddle-point (mean-field approximation), Goldston mode etc. have been followed in order to simplify the action and hence Lagrangian density. The Lagrangian density, which are of solely the function of phase differences across the junction barrier, is minimized to derive the system of perturbed sine-Gordon equations which help to explain the phase dynamics of the junction system. In the present work, the system of sine-Gordon equations are established for the stack of long Josephson junction based on multi-gap superconductors and then applied for two-gap superconductor like MgB 2 . The generalized sine-Gordon equations for stack of LJJ are used to explain the phase dynamics in the single and double (coupled) LJJ. The system of perturbed sine-Gordon equations, for single and double junctions, have been solved numerically using the finite difference approximation, assuming the solution of unperturbed sG equation as the initial condition. The Neumann boundary condition has been maintained so that the kink or anti-kink can reflect at the boundary. The dynamics of phase differences have been observed for different layer and junction thicknesses and found that the motion of kink or anti-kink, which also represents the fluxon or anti-fluxon, is found to be more complicated as time goes on. During the motion, it has been observed that fluxons and anti-fluxon are created and superposed to each other. As a result, phase locked and anti-locked situation have been observed. The Josephson part of Lagrangian density has been computed and minimized in the domain length at each time step. In order to study the phase frustration, the minimized energy is plotted as the function of time in addition to the corresponding phase differences. It is found that 2 the phase frustration occurs quickly for higher layer and junction thicknesses. It is also observed that the phase frustration occurs at low time for higher tunnel voltage. The current-voltage characteristics have also been studied by computing the average current flowing out across the junction system at different tunnel voltages. The current-voltage characteristics in coupled LJJ is found to be linear at very low tunnel voltage, slightly non-linear with positive differential resistance up to certain tunnel voltage depending on the junction geometry and completely non-linear for higher ones irrespective to the junction geometry. But the nature of the non-linearity solely depends of junction geometry i.e. thicknesses of the barrier and superconducting layer. In some non-linear regions, the negative differential resistances are observed which confirms that the device behaves as source or radiation chamber. The negative resistance may arise due to the non-dissipative transition of quasi-particles (i.e. fluxons or anti-fluxons) in the system. Due to this peculiar nature, the device is applicable to the low temperature electronic devices which demands the negative resistance.