Jamie Le Signe, Robert Brown PhD Scholar

PhD Physics

Dear Mr Brown,

As always, I hope both you and your family are well. Since my last update I have struck a particularly productive vein of work and would like to share my progress with you.

Prior to my last update I had begun work on ‘suspended-parallel Josephson arrays’, which are the logical extension of a mechanical SQUID. An example of such an array in a ‘ring’ configuration is shown below. Each Josephson junction is composed of a suspended weak link, which we have studied in detail previously.

The ring is topologically different to open-ended arrays, in that magnetic flux quanta can be trapped within the system. This introduces topological ‘fluxons’ into the system, that can propagate resonantly around the ring to create a fluxon resonance. This effect is the focus of our paper ‘Driving and cloaking mechanical resonators from topological fluxons in a Josephson junction parallel ring array’, which will hopefully be submitted soon (alongside the single-junction paper that has been complete for years…). In this paper we show how topological fluxons can drive mechanical resonance, manifested as a plateau in the DC IV curve. We investigate how mechanical resonance interacts with the fluxon resonance, finding that it leads to a tuneable mechanical Fano-resonance, and a complex network of interconnected hysteresis loops (as shown below). Finally, we find a striking feature wherein the mechanical resonators are completely cloaked from the fluxon at a particular voltage. This work is complete, but is very difficult to explain succinctly, and I am perpetually editing the paper to make it more comprehensible. If you would like to read a preliminary copy, please do not hesitate to ask.

Inspired by the ring, I started work on an open-ended array. Open-boundaries prevent the trapping of fluxons but introduce the possibility of exciting the waveguide modes of the array, or ‘Fiske modes’. By introducing mechanical coupling, I find that an array of N junctions contains N pairs of electrical and mechanical resonances. The electrical resonances are the regular Fiske modes, whilst the mechanical resonances form a band of Fano-resonances. The case N=2 reduces to a mechanical SQUID, where old and new theories unify. I believe that this result could form a quick satellite paper in a technical journal, once appropriate figures have been produced.

This leads us to my most recent work. By introducing an elastic interaction between the mechanical resonators, I form a discrete model of a wide suspended junction, such as a suspended sheet of graphene (as opposed to the one-dimensional suspended carbon nanotube). This discrete model can be used to numerically simulate the continuum case, and preliminary simulations confirm that mechanical Fiske modes can be excited. This means that I can selectively excite the mechanical normal modes of graphene using only DC current bias and moderate magnetic fields. This presents a relatively simple method of achieving a beautiful and novel result, which I hope to publish and present to a wide audience.

Once again, I would like to thank you for your continued financial support. Your generosity has enabled me to live comfortably and focus exclusively upon my research. I appreciate this immensely and hope my published works and thesis will reflect my gratitude. Best wishes, Jamie