Resonance Phenomena in Coupled Josephson Junctions Hazem Mohamed Mahmoud Abdelhafiz

Supervisor: Wael Akl

Thesis (M.A.)—Nile University, Egypt, 2013 .

"Includes bibliographical references"

Contents:
2 Theoretical Study 14
2.1 Coupled Superconductors . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Electron Tunneling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Josephson equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.4 The Josephson critical current Ic . . . . . . . . . . . . . . . . . . . . . . . 22
3 Computational methods 24
3.1 Runge-Kutta Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.1 Second-Order method . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.1.2 Fourth-Order Methods . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2.1 Capacitively coupled Josephson junctions (CCJJ) . . . . . . . . . . 26
iii
Contents iv
3.2.2 Capacitively coupled Josephson junctions with diffusion current
(CCJJ+DC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.3 System of equations of IJJ . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4 Results and Discussion 35
4.1 Charge density wave in IJJ . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2 Dynamics of transition LPW → CDW . . . . . . . . . . . . . . . . . . . . 36
4.3 Transformations CDW → CDW . . . . . . . . . . . . . . . . . . . . . . . 37
4.4 Radiation effect on IJJ . . .

Abstract:
We demonstrate the creation of a charge density wave (CDW) along a stack of coupled
Josephson junctions in layered superconductors. Electric charge in each superconducting
layer oscillates around some average value, forming a breathing CDW. We show the
transformation of a longitudinal plasma wave to a CDW in the state corresponding to
the outermost branch. Transitions between different types of CDW’s, related to the
inner branches of current voltage characteristics, are demonstrated. We will show the
effect of radiation on the CDW and the appearance of Shapiro steps in the inner branch.

Text in English, abstracts in English and Arabic