Second-Harmonic Current-Phase Relation in Josephson Junctions with Ferromagnetic Barriers

Abstract

We report the observation of a current-phase relation dominated by the second Josephson harmonic in superconductor-ferromagnet-superconductor junctions. The exotic current-phase relation is realized in the vicinity of a temperature-controlled 0-to-π junction transition, at which the first Josephson harmonic vanishes. Direct current-phase relation measurements, as well as Josephson interferometry, non-vanishing supercurrent and half-integer Shapiro steps at the 0-π transition selfconsistently point to an intrinsic second harmonic term, making it possible to rule out common alternative origins of half-periodic behavior. While surprising for diffusive multimode junctions, the large second harmonic is in agreement with theory predictions for thin ferromagnetic interlayers.

Evidence of half-integer Shapiro steps originated from nonsinusoidal current phase relation in a short ballistic InAs nanowire Josephson junction

“…We note that the observed half-integer steps are not related to the 0-π transition of the junction, which also generates halfinteger steps as reported in previous research [18][19][20]. The 0-π transition can be invoked in a Josephson junction with the time-reversal symmetry broken [45,46] or the quantumdot Josephson junctions [47][48][49][50].…”

“…Since the 2000s, the fractional steps have also been observed in the Josephson junctions whose skewness of the CPR can be controlled by some parameters. In the case of superconductor (SC)-ferromagnet-SC junctions, the CPR holds huge higher-order components only in the vicinity of the 0-π transition temperature or thickness and the half-integer steps appear only in the vicinity [18][19][20]. Experimental studies on such controllable junctions are available to elucidate the origin of the half-integer steps.…”

Superconducting Circuits without Inductors Based on Bistable Josephson Junctions

“…Notably, the disappearance of the first harmonic here leads to a doubling of the CPR. In this case, the JJ is called 2φ-JJ [33][34][35][36][37]. If the second-harmonic amplitude is negative, B < 0, the JJ's energy minima are symmetrically located around zero at ±φ phases, where |φ| ≤ π/2 [29].…”

Magnetic Josephson Junctions: New Phenomena and Physics with Diluted Alloy, Conventional Ferromagnet, and Multilayer Barriers

“…Although the theoretical concept of the π-state in the ferromagnetic Josephson junctions have been proposed by Buzdin in 1982 [4], a number of experimental reports have been presented since 2000. The key for successful demonstration of ferromagnetic Josephson junctions was to adopt "weak" ferromagnetic alloys for the barrier of the junction [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23]. The surviving length of the order parameters penetrating into the ferromagnetic barrier is characterized by the coherence length in the ferromagnet, .…”

“…The authors also investigate a possibility of the higher-order harmonics predicted in metallic Josephson junctions, and concluded that there was no higher-order harmonics for the junctions. Later, the existence of the second-order harmonics for the Cu0.52Ni0.48, Cu 0.47 Ni 0.53 and Cu 0.4 Ni 0.6 barrier junctions was reported based on systematic measurements of the temperature dependence of the critical current, Shapiro step, and Fraunhofer pattern [21][22][23].…”