# Publications

List of Papers, Presentations and Conferences Attended.

## Novel results obtained by modeling of dynamic processes in superconductors

June 15th, 2022

Based on the time-dependent Ginzburg-Landau system of equations and finite element modeling we present novel results related with physics of phase-slippage in superconducting wires surrounded by a non-superconductive environment. These results continue our previously reported modeling approach related to superconducting rings and superconductive gravitational wave detector transducers. It is shown that the phase-slip centers (PSCs) can be effective in originating both positive and negative thermal fluxes. With an appropriate design utilizing this nonequilibrium physics, cooling below 1K is possible to achieve.

## Violation of magnetic flux conservation by superconducting nanorings

December 9, 2021

The behavior of magnetic flux in the ring-shaped finite-gap superconductors is explored from the view-point of the flux-conservation theorem which states that under the variation of external magnetic field "the magnetic flux through the ring remains constant" (see, e.g., [L.D. Landau and E.M. Lifshitz, Electrodynamics of Continuos Media, vol. 8 (New York, Pergamon Press, 1960), Section 42]). Our results, based on the time-dependent Ginzburg-Landau equations and COMSOL modeling, made it clear that in the general case, this theorem is incorrect. While for rings of macroscopic sizes the corrections are small, for micro and nanorings they become rather substantial. The physical reasons behind the effect are discussed. The dependence of flux deviation on ring sizes, bias temperature, and the speed of external flux evolution are explored. The detailed structure of flux distribution inside of the ring opening, as well as the electric field distribution inside the ring's wire cross section are revealed. Our results and the developed finite element modeling approach can assist in elucidating various fundamental topics in superconducting nanophysics and in the advancement of nanosize superconducting circuits prior to time-consuming and costly experiments.

## Gravitational wave sensors based on superconducting transducers

November 8, 2021

Following the initial success of LIGO, new advances in gravitational wave (GW) detector systems are planned to reach fruition during the next decades. These systems are interferometric and large. Here we suggest different, more compact detectors of GW radiation with competitive sensitivity. These nonresonant detectors are not interferometric. They use superconducting Cooper pairs in a magnetic field to transform mechanical motion induced by GW into detectable magnetic flux. The detectors can be oriented relative to the source of GW, so as to maximize the signal output and help determine the direction of nontransient sources. In this design an incident GW rotates infinitesimally a system of massive barbells and superconducting frames attached to them. This last rotation relative to a strong magnetic field generates a signal of superconducting currents. The suggested arrangement of superconducting signal sources facilitates rejection of noise due to stray electromagnetic fields. In addition to signal analysis, we provide estimates of mechanical noise of the detector, taking into account temperature and elastic properties of the loops and barbells. We analyze at which parameters of the system a competitive strain sensitivity could be achieved. We have tested the basic idea of the detector in the laboratory and reached the theoretical Johnson-Nyquist noise limit with multiturn coils of normal metal. Realization of full-blown superconducting detectors can serve as viable alternatives to interferometric devices.

## Phonon Feedback Effects on Dynamics of Phase Slip Centers in Finite Gap Superconductors

July 2, 2020

The results on the behavior of phase-slip centers in thin superconducting wires based on finite-element modeling and time-dependent Ginzburg-Landau (TDGL) equations are discussed. For closer relationship with experiments, we used finite-gap formulation of the TDGL system. Both the dynamic equation for the Cooper-pair condensate wave-function and the expression for the electric current are more complex than in the gapless case. On this basis, the influence of nonequilibrium phonons is explored. These phonons can essentially change the location of geometrical points in which the phase slippage takes place. They also affect the frequency of phase-slip oscillations. The reported effects are experimentally detectable and can be used in practical devices.

## Visualization and Exploration of the Dynamics of Phase Slip Centers in Superconducting Wires

October 4th, 2019

The dynamics of phase slip centers in a 1D model of superconducting wire was created based on the set of time-dependent Ginzburg-Landau equations (TDGL). COMSOL Multiphysics®’ General Form PDE interface was used. TDGL has successfully applied to this problem decades ago and most recently, the visibility of solutions has been enhanced by engaging COMSOL's power. The feature which distinguishes the current report here is that, for the first time, the set of TDGL equations for superconductors with finite gap was used in full. The terms relevant to the presence of finite gap were included not only into the equation for the wave function of the condensate, but also into the equation for the current in the form of interference terms.

The performed thorough study of the solutions of these non-linear equations required extensive searches for multiple solutions at certain values of given parameters. We found it extremely helpful using the built-in capability of COMSOL which could be operated in tandem with MATLAB®. By developing the MATLAB code, we were able to automate findings of the relevant solutions. We obtained "branching" and "anti-branching" of these solutions at certain parameters of the problem. These properties are directly relevant to experimental results obtained with these objects.

Evolution of phase-slip centers takes place in picosecond time-scale, which can be very hard to visualize in practice. COMSOL's ability to generate animation provides unique opportunities to trace details of the microscopic evolution of various observables (such as the Cooper-pair density, superfluid and normal velocities, etc.).

## Conferences

8th International Workshop on Numerical Modelling of High Temperature Superconductors - Nancy, France June 2022, Presenter

New Directions in Function Theory: From Complex to Hypercomplex to Non-Commutative - Chapman University, November 2019

COMSOL Conference - Boston October 2019, Presenter

APS March Meeting - Boston 2019

PIMan Workshop - Chapman University, March 2019

APS Far West Fall Meeting - Cal State Fullerton, October 2018

7th International Workshop on Quantum Simulation and Quantum Walks - Chapman University, March 2018