Sakhniuk P. Electrodynamic properties of tunnel Josephson junctions with anharmonic current-phase relation

Sakhniuk P. V. Electrodynamic properties of tunnel Josephson junctions with anharmonic current-phase relation. — Qualifying scientific work on the rights of the manuscript. Thesis for the Degree of Doctor of Philosophy on specialty 104 — Physics and Astronomy. — Lesya Ukrainka Volyn National University, Lutsk, 2026. The dissertation is devoted to the study of macroscopic quantum coherence and the development of a theoretical model of electrodynamic and magnetic characteristics, nonlinear phase evolution, and the conditions for the occurrence of the Josephson diode effect in tunnel superconductor-insulator-superconductor (SIS) junctions. The main emphasis is placed on systems with high quantum-mechanical transparency of the dielectric barrier near the critical temperature (Tc). Under these conditions, the Ginzburg-Landau coherence length increases, and the spatial distribution of the order parameter becomes extremely sensitive to the macroscopic motion of current carriers. This causes depairing effects of the Cooper pair condensate, generates strong anharmonicity, and renders the classical sinusoidal Josephson model insufficient. Chapter 1 provides a literature review on the fundamental problems of phase coherence, analyzes the limits of applicability of the standard harmonic model, and examines the physical nature of depairing effects and the mechanisms underlying the diode effect. Chapter 2 contains a microscopic derivation of the linear integral equation for the order parameter in an SIS junction using the Green's function method. By applying the method of quasi-orthogonality to asymptotics, correct boundary conditions for the Ginzburg-Landau equation are found, and a generalized non-sinusoidal current-phase relation is obtained, the key change of which is second-harmonic generation. Chapter 3 is devoted to macroscopic magnetic properties. It is proven that second-harmonic generation causes a steeper decay of the critical current in weak magnetic fields, increasing magneto-field sensitivity. For long Josephson junctions, the deformed profile and the rest energy of the fluxon are calculated. Chapter 4 constructs generalized dynamic models to describe nonlinear phase evolution. Mechanical analogies are substantiated: the motion of a pendulum with a variable suspension length and the motion of a particle in a logarithmically deformed potential landscape, which increases the restoring force and the plasma frequency of oscillations, making it useful for optimizing phase qubits. Chapter 5 describes the conditions for the occurrence of the Josephson diode effect in planar structures near the critical temperature. It is established that the non-reciprocity of critical currents requires a combination of a magnetic field and a critical current density gradient, and the diode effect itself arises only in the presence of higher current harmonics. In conclusion, the developed theoretical framework allows for optimizing the parameters of superconducting qubits, improving the resolution of supersensitive magnetometers, and creating dissipationless cryogenic rectifiers and memory elements.