Time-domain simulator of Josephson junctions based on the BCS theory

TL;DR

This paper presents a time-domain simulator for Josephson junctions based on BCS theory, enabling detailed analysis of their dynamic behavior under various conditions, including microwave signals and different materials.

Contribution

The authors developed a novel time-domain simulator incorporating BCS theory to analyze Josephson junctions' behavior with high physical accuracy.

Findings

Simulated I-V hysteresis depending on McCumber parameter.

Modeled Shapiro steps under microwave irradiation.

Assessed MgB2 junctions at THz frequencies considering anisotropic gaps.

Abstract

We realized a time-domain simulator based on the electrodynamics of Cooper pairs and quasiparticles in Josephson junctions. The tool, based on the charge carriers' densities of states described by the Werthamer and Harris formalisms of Bardeen-Cooper-Schrieffer (BCS) theory, allows to analyze the behavior of current- or voltage-controlled Josephson junction-based circuits for any signal waveform, at a physical temperature comprised between the absolute temperature and the critical temperature. The simulator can account for I-V curve hysteresis depending on the McCumber parameter, or Shapiro and photo-assisted steps in the presence of a monochromatic microwave signal. We used the simulator to assess the behavior of MgB2-based Josephson junctions at THz frequencies by taking into account the presence of the two anisotropic gaps of MgB2.