Modeling-based prediction of current oscillation with the Josephson frequency in voltage-biased phase-slip center filaments

Abstract In this article, we demonstrate that the voltage-biased phase-slip center (PSC) can act as a direct equivalent (not merely an analogy) of the Josephson effect in Josephson junctions (JJs). We analyze the behavior of PSCs in the case when a constant voltage V is applied to the superconducting filament. The analysis is performed using finite element modeling on the basis of time-dependent Ginzburg–Landau (TDGL) equations. It reveals that the current in the filament oscillates with the Josephson frequency $$\omega =2eV/\hbar $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>=</mml:mo> <mml:mn>2</mml:mn> <mml:mi>e</mml:mi> <mml:mi>V</mml:mi> <mml:mo>/</mml:mo> <mml:mi>ħ</mml:mi> </mml:mrow> </mml:math> . This fact may have important corollaries in practice.