Modeling Superconducting Wires and Determining the Impact of Nonlocal Electrodynamics – with a Surprising Twist!


Quantum computing exploits quantum-mechanical phenomena, such as superposition and entanglement, to perform certain computational tasks much faster than conventional “classical” computers. While quantum computers are difficult to build, there has been astounding progress in the use of cryogenic superconducting circuits as a platform for quantum hardware. For instance, superconducting devices built specifically for quantum annealing, containing over 2000 qubits, have been developed and are currently being benchmarked against classical algorithms. Recent studies have also reported on universal quantum circuits containing nine qubits with over 1000 quantum logic gates.

While the design of these circuits requires careful control of superconducting circuit parameters such as self- and mutual inductances, Josephson critical currents, capacitances, etc., most of the design work has so far been done without the numerical prediction of circuit parameters. This has happened because the tools for numerical modeling of superconducting circuits are much scarcer, in contrast to the tools available to the semiconductor industry. Consequently, more numerical research-oriented studies in superconducting electronics are highly desired.

In a recent research paper published in Physical Review Applied, University of Victoria scientists led by Professor Rogério de Sousa from the Department of Physics and Astronomy put forth a novel approach with which they conducted exact numerical calculations of the current density and vector potential for superconducting wires in the nonlocal regime, which is common to a large variety of superconducting materials being used in superconducting device technology. In their study, the researchers showed that the usual approximation of local electrodynamics generally breaks down, impacting circuit parameters such as inductance and flux noise.

Briefly, the team presented analytical solutions for the current density and vector potential inside a wire using the approximation of local electrodynamics. Next, they presented their numerical method for exact solution of the self-consistent relations arising in nonlocal electrodynamics, and compared their exact result to the local theory and to simple approximations based on an effective penetration depth. Lastly, they presented calculations of inductance and flux noise due to impurities at the surface and the bulk of the wires.

The authors observed that in the presence of nonlocal effects, vector potential and current density changed sign inside the wire, due to self-induced overscreening, which occurred solely due to the fields produced by the supercurrent, without an applied external field. The scientists also noted that nonlocal electrodynamics had a large impact on device properties such as inductance and flux noise. For example, in local superconductors the kinetic inductance was always greater than the internal inductance, with the opposite being observed for nonlocal superconductors. The authors expect that these effects will play an important role in all circuits based on superconducting materials in the nonlocal regime, such as aluminum superconductors with a large electron mean free path.

And then there was an interesting twist. The first author of the paper, graduate student Pramodh Yapa, a music and dance aficionado, decided that the best way to explain his work was to depict electrons as unsociable dancers who suddenly become joyful once paired up in superconducting Cooper pairs. So he wrote original song and dance choreography describing how electrons behave in a nonlocal superconducting wire. His video won first place in the “Dance your Ph.D.” contest promoted in 2019 by Science magazine, and was depicted by several media outlets such as the National Public Radio and Forbes magazine.

Modeling Superconducting Wires and Determining the Impact of Nonlocal Electrodynamics - with a Surprising Twist! - Advances in Engineering
Depicts the current density in a cylindrical superconducting wire, with varying Pippard coherence length ξ. The London penetration depth λ was assumed fixed. Note how the current becomes less localized around the surface as ξ increases.

About the author

Rogério de Sousa is Associate Professor at the Department of Physics and Astronomy and member of the Centre for Advanced Materials and Related Technology at the University of Victoria, British Columbia, Canada.

He received the B.Sc. and M.Sc. degrees in Physics from the State University of Campinas, Brazil in 1997 and 1998, respectively, and the Ph.D. degree from University of Maryland, College Park in 2003. His Ph.D. thesis advisor was Prof. Sankar Das Sarma, and the topic was related to the impact of decoherence on the implementation of spin-based quantum computers using semiconductor materials. From 2003 to 2007 he was a postdoctoral fellow at the University of California, Berkeley in the groups of Prof. Birgitta Whaley in the Dept. of Chemistry and Prof. Joel Moore in the Dept. of Physics. During this time he worked on several theoretical problems related to coherence control, decoherence and noise in metallic and superconducting devices, as well as electrical control of magnetism and optical properties of multiferroic materials.

Since 2007 he is faculty at University of Victoria where he conducts research on the physics of materials and devices, with applications to quantum computing and spintronics. de Sousa is the leader of a Natural Sciences and Engineering Research Council of Canada (NSERC) Collaborative Research and Development project with D-Wave Systems Inc., investigating the possible sources and effects of magnetic flux noise in the D-Wave quantum annealing processor.

About the author

Pramodh Senarath Yapa is a Ph.D. Student in the Department of Physics and a member of Quantum Alberta at the University of Alberta, AB, Canada. His current research area is quantum many-body theory, under the supervision of Professors Joseph Maciejko and Frank Marsiglio, with a focus on superfluid Helium-3 and the exotic phases it forms in confined geometries. He received his M.Sc. in Condensed Matter Theory at the University of Victoria, British Columbia, Canada in 2017, and his B.Sc. at Carleton University, Ontario, Canada in 2015.

His M.Sc. research was conducted under the supervision of Professor Rogério de Sousa, studying non-local superconductivity and its effects on superconducting devices for quantum computing applications. Due to his keen interest in Science communication, Pramodh was awarded the 2018 Dance Your PhD award for adapting his M.Sc. thesis into a 3-act musical. He can be found on social media under @yapapramodh.


Pramodh Senarath Yapa, Tyler Makaro, Rogério de Sousa. Impact of Nonlocal Electrodynamics on the Flux Noise and Inductance of Superconducting Wires. Physical Review Applied, volume 11, 024041 (2019)

Go To Physical Review Applied

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