Absence of fractional giant Shapiro steps in diagonal Josephson-junction arrays

Abstract

When rf and dc bias currents are injected diagonally into an NxM Josephson-junction array and a

Giant Shapiro resonances in a flux-driven necklace of Josephson junctions

“…Motivated by significant advances in microfabrication techniques of Josephson junction (JJ) arrays, many contemporary studies have focused on understanding the dynamic response of two-dimensional JJ arrays [1][2][3][4][5][6][7]. One type of array with well-defined uniform properties is made of superconducting-normal-superconducting (SNS) proximity effect junctions.…”

“…Several novel collective locked-in states have been discovered which are manifested in the current versus voltage (IvsV ) characteristics as plateaus. These giant Shapiro steps are a macroscopic manifestation of diverse underlying collective vortex oscillating states [1][2][3][4][5].…”

“…Most recent studies, experimental and theoretical [1][2][3][4][5]7], have considered current driven two-dimensional JJ arrays. In this paper we study the dynamic response of a ring of N equally spaced JJ, referred to as a Josephson Junction Necklace (JJN), driven by a perpendicular external time-dependent flux Φ e (t), including self-induced magnetic field effects.…”

Energy gap and tunneling

“…The circuit consists of the usual Josephson current I c sinφ in parallel with a conductance G. In addition, it has as inputs a dc source current I 0 and an rf source current I s cos ω s t, with the total source current I given by IðtÞ 5 I 0 1 I s cos ω s t: for comparison. This staircase pattern, which is referred to as Shapiro steps (Eikmans and van Himbergen, 1991;Shapiro, 1963;Yu et al, 1992), has been reported by many observers (e.g., Kriza et al, 1991;Kvale and Hebboul, 1991;Larsen et al, 1991;Lee et al, 1991;Sohn et al, 1991).…”

Non-Equilibrium Coherent Vortex States and Subharmonic Giant Shapiro Steps in Josephson Junction Arrays

“…This interpretation was successfully verified in numerical simulation modelling of the arrays by a resistively shunted junction (RSJ) model 7,8 , as well as from analytic studies 9 . There have also been some experimental 10 and theoretical studies 11,12,13 of the relevance of the geometry of the arrays and the direction of the input current on the generation of fractional GSS. Moreover, the experiments in GSS have encouraged investigations of JJA as coherent radiation sources 14 .…”