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Physical review. B./Physical review. B

Missing Shapiro steps in nonhysteretic Josephson junction with 2 π periodic supercurrent

S. S. Ustavschikov, Denis Yu. Vodolazov

Published Nov 14, 2024• 2 citations
Publisher

Abstract

We theoretically demonstrate that in a nonhysteretic Josephson junction (JJ) with a $2\ensuremath{\pi}$ periodic supercurrent in the presence of radio-frequency (RF) radiation one or several low-lying Shapiro steps could be absent in the voltage-current $(VI)$ characteristic. The effect exists at low RF power and at frequencies $f$ approximately ten times smaller than ${f}_{0}={I}_{c}{R}_{N}/{\mathrm{\ensuremath{\Phi}}}_{0}$ (where ${I}_{c}$ is the critical current, ${R}_{N}$ is the normal-state resistance of the Josephson junction, and ${\mathrm{\ensuremath{\Phi}}}_{0}$ is the magnetic flux quantum). The origin of the effect is related to the large differential resistance ${R}_{\mathrm{diff}}=dV/dI$ near $I\ensuremath{\simeq}{I}_{c}$, which is significantly greater than the value predicted by the resistively capacitance shunted junction (RCSJ) model in the overdamped limit. Our theoretical results are supported by experiments on Nb/NbSi/Nb Josephson junctions with nonhysteretic $VI$ curves, where we observe the absence of one or more low-lying Shapiro steps, depending on the frequency and power of the RF radiation.

DOI
10.1103/physrevb.110.184511

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We theoretically demonstrate that in a nonhysteretic Josephson junction (JJ) with a 2\ensuremathπ2\ensuremath{\pi}2\ensuremathπ periodic supercurrent in the presence of radio-frequency (RF) radiation one or several low-lying Shapiro steps could be absent in the voltage-current (VI)(VI)(VI) characteristic. The effect exists at low RF power and at frequencies fff approximately ten times smaller than f0=IcRN/\ensuremathΦ0{f}_{0}={I}_{c}{R}_{N}/{\mathrm{\ensuremath{\Phi}}}_{0}f0​=Ic​RN​/\ensuremathΦ0​ (where Ic{I}_{c}Ic​ is the critical current, RN{R}_{N}RN​ is the normal-state resistance of the Josephson junction, and \ensuremathΦ0{\mathrm{\ensuremath{\Phi}}}_{0}\ensuremathΦ0​ is the magnetic flux quantum). The origin of the effect is related to the large differential resistance Rdiff=dV/dI{R}_{\mathrm{diff}}=dV/dIRdiff​=dV/dI near I\ensuremath≃IcI\ensuremath{\simeq}{I}_{c}I\ensuremath≃Ic​, which is significantly greater than the value predicted by the resistively capacitance shunted junction (RCSJ) model in the overdamped limit. Our theoretical results are supported by experiments on Nb/NbSi/Nb Josephson junctions with nonhysteretic VIVIVI curves, where we observe the absence of one or more low-lying Shapiro steps, depending on the frequency and power of the RF radiation.
We report an experimental and theoretical study of low-voltage resistive states observed in small tunnel Josephson junctions subject to microwave radiation. The observed features result from Shapiro steps in the current–voltage characteristics and appear when both thermal fluctuations and high frequency dissipation are strong. Without microwave radiation, Josephson junctions have a phase diffusion supercurrent branch characterized by a finite small resistance and hysteretic switching to a higher voltage range under these conditions. When microwave radiation is applied, three different types of resistive states are observed in the current-voltage characteristics. First, a phase diffusion branch steadily evolves and its maximum voltage Vm increases with the microwave power. Another interesting observed feature is a zero-crossing resistive state characterized by a negative resistance. Finally, we find that the low-voltage resistive state can split into numerous hysteretic fine branches resembling incoherent Shapiro-like steps. The appearance of a particular resistive state depends on the interrelations among the Josephson energy EJ, the energy kBT of thermal fluctuations, and the microwave frequency ω. A theoretical analysis based on incoherent multi-photon absorption by a junction biased in the Josephson phase diffusion regime is in good agreement with the experimental observations.
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The current height of RF-induced voltage steps in nonhysteretic single Josephson junctions is usually a small fraction of the critical current. It is demonstrated that when a resistively shunted DC superconducting quantum interference device (SQUID) is subjected to an RF magnetic flux, a voltage step with a large current height is obtained. In contrast to weak selection rules for single Josephson junctions, strong selection of the step harmonic number occurs in a shunted DC SQUID for appropriate choice of RF amplitude and DC flux offset, with odd harmonic numbers selected by half-integer flux quantum offsets and even harmonic numbers by integer flux quantum offsets. This pronounced effect has immediate implications for voltage standards and fast, high-precision digital-to-analog converters.>
Abstract The method of numerical solution of equations is used within the resistive model to study the behavior of deviations of the current‒voltage characteristics of nonideal Josephson junctions from similar characteristics of ideal (standard) junctions. Nonideal Josephson junctions are those in which the current‒phase relation contains additional Josephson harmonics. The dependences of the amplitudes of current steps (Shapiro steps) on the power of external electromagnetic radiation is calculated. The shape of these dependences is shown to deviate from the corresponding dependences for ideal Josephson junctions. In addition, the paper examines the features of the occurrence of additional current steps on the current‒voltage characteristics of Josephson junctions and shows a possibility of their absence in the case of the presence of additional harmonics in the current‒phase relation. The obtained results prove that by analyzing the step structure of the current‒voltage characteristics it is possible to obtain information about the properties of Josephson junctions and superconductors that form them.
High Tc Josephson junctions have IcRn products as large as a few mV at liquid helium temperature, and hence, the frequency normalized by IcRn∕Φ0 becomes on the order of 10−3 for a gigahertz (GHz) microwave signal. (Here, Ic, Rn, and Φ0 are the critical current, the normal resistance, and a flux quantum, respectively.) It is well known that a microwave-current-driven Josephson junction does not exhibit clear Shapiro steps under such low frequency conditions. Instead of Shapiro steps, however, we often observe a current-step-like structure in the current–voltage curve of YBa2Cu3O7−δ grain boundary Josephson junctions coupled to a GHz signal. In this article, we present a model analysis for such current-step-like structures. Two types of device models are employed: a simple resistively and capacitively shunted junction model and a rf-field-driven two-junction superconducting quantum interference device model. Numerical results of the latter model agree with the experimental results, which indicates that the envelope of small Shapiro steps, including the effects of microwave-induced motion of flux quanta, appears as a current-step-like structure in a high Tc Josephson device coupled to a GHz microwave.