#### PI: Karl Berggren, Department of Electrical Engineering & Computer Science, MIT

PI: Mikhail Skvortsov, Center for Photonics and Quantum Materials, Skoltech

Task 1: Suppression of superconductivity in disordered films: theoretical studies of the critical temperature due to the combined effect of disorder and interaction originating both from large and short scales. Determine the limits of applicability of the Finkelstein theory. Correlate theoretical predictions with available experimental data.

Task 2: Spontaneous inhomogeneity of the superconducting state: quantitative description of emergent inhomogeneity in disordered superconducting films. Study of its influence on various measurable properties: density of states, superfluid density, and frequency-dependent complex conductivity.

Task 3A: Superconducting current corner crowding: development of high-coherencelength aluminum patterns and testing of various geometries and correlation to theory.

Task 3B: Superconducting current corner crowding: numerical simulation of the current pattern based on self-consistent solution of Bogolyubov-de-Gennes and Usadel equations.

Task 4A: Controlled frustration of current flow in a cross: study the relationship between the critical current of a wire and the current crossing it. Determine if expected periodicity appears associated with trapping of quantized flux in the corner structure. Correlate this with theoretical predications.

Task 4B: Controlled frustration of current flow in a cross: numerical simulation of the current pattern based on self-consistent solution of Bogolyubov-de-Gennes and Usadel equations.

Task 5: Measurements of kinetic inductance as a function of DC current bias and temperature and microwave effects on the switching and retrapping current in amorphous superconducting nanowires.