Loughborough University
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Ratchet effects, flux flow resonances and Shapiro steps in Josephson junction arrays

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posted on 2020-06-22, 08:44 authored by Jonathan Cox
Josephson junctions (JJs) have become an integral component in superconducting electronics due to their non-linear response, sensitivity to magnetic fields and microwaves and the ability to generate high frequency electromagnetic radiation.

This thesis investigates three phenomena of JJ arrays; the ratchet effect, flux flow resonances and Shapiro steps. A simulation model (which is similar to discrete Josephson transmission line) was used extensively to explore what consequence
a) multiple array parameters such as the size of the superconducting loops separating the JJs, array spatial asymmetry, number of JJs in the array, structural fluctuations of the array due to imperfections of fabrication or intrinsic inhomogeneity of the Josephson critical current along the array;
b) or junction parameters such as junction widths, junction critical currents;
c) or finally thermal fluctuations due to the finite temperature of operation have on these three effects, as such this thesis is split into three parts.

In the presence of an externally applied magnetic field, ratchet effects have been reproduced numerically in the current voltage characteristics (IVCs) of asymmetric JJ arrays. Firstly, the ratchet efficiency of several arrays was simulated and found that each array design has a unique pattern of efficiency which could be reversed and tuned by changing the applied magnetic field. Larger efficiencies could be achieved with larger numbers of JJs in the array. Larger arrays were able to withstand more amounts of noise than smaller arrays.

Flux flow resonances have been reproduced numerically on the IVCs of the JJ arrays for multiple values of applied magnetic field. The derivatives (dI/dV) have been investigated in detail. The spatial asymmetry of the arrays has a large influence on the flux flow resonance produced by the JJ arrays, with each design producing a different pattern of resonances. The number of junctions in an array also has an effect on the resonances, the voltage location of smaller arrays show periodic oscillations with magnetic field whereas larger arrays do not, the resonance voltage and dI/dV locations increases to a maximum and levels out. Simulations also showed that the magnetic field around each insulating loop for larger arrays had distinct distribution around specific holes.

Integer and fractional Shapiro steps were reproduced numerically on the IVCs of the JJ arrays. When analysing Shapiro steps, DC and AC magnetic field and / or AC current were applied. The voltage steps appeared in different preferences for steps with positive or negative voltages. It was found that larger steps were a result of the phase difference across the JJs being in phase with each other. An alternating magnetic field was applied to the arrays which produced similar steps caused by the induced current within the array. Combining both AC current and an alternating magnetic field resulted in pumping between the two effects leading to larger steps when the frequencies of both coincide.

For the case of ratchet effects and flux flow resonances a detailed qualitive comparison was made with experimental data of JJ arrays made of yttrium barium copper oxide (YBCO).


Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Partnership



  • Science


  • Physics


Loughborough University

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© Jonathan Stuart Cox

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A doctoral thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.


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Boris Chesca ; Sergey Saveliev

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  • PhD

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  • Doctoral

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