Analysis of a Resistive-Capacitive Shunted Josephson Junction with Topologically Nontrivial Barrier Coupled to a RLC Resonator

Abstract

This paper presents the resistive-capacitive shunted Josephson junction (RCSJJ) with a topologically nontrivial barrier (TNB) coupled to a linear RLC resonator. The rate equations describing RCSJJ with TNB coupled to the linear RLC resonator are established via Kirchhoff’s current and voltage laws. The model exhibits four, two, or no equilibrium points depending on the external direct current (DC) source and the fractional parameter. The stability analysis of the equilibrium points with credit to the Routh-Hurwitz stability criterion reveals that the stability of equilibrium points depends on the DC source and the fractional parameter. Current-voltage characteristic reveals the presence of a birhythmicity zone which is sensitive to the fractional parameter m. As the fractional parameter increases, the coexistence of the resonant state is destroyed, which is followed simultaneously by the appearance of a new resonance state. Depending on initial conditions, birhythmic behaviour is characterized by the existence of a limit cycle. The projection of the phase space in the specific plane and the time evolution of charge is predicted in which the amplitude of attractors reported is sensitive to the parameter m. Lastly, with a defined fractional parameter, the amplitude of the branch locked to the resonator is greater than the unlocked branch.