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arXiv:1806.10420 · Physical Review Applied

Existence of Shapiro Steps in the Dissipative Regime in Superconducting Weak Links

Connor D. Shelly, Patrick See, Ivan Rungger, Jonathan M. Williams

Published Feb 26, 2020• 20 citations
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Abstract

We present measurements of microwave-induced Shapiro steps in a superconducting nanobridge weak link in the dissipative branch of a hysteretic current-voltage characteristic. We demonstrate that Shapiro steps can be used to infer a reduced critical current and an associated local temperature. Our observation of Shapiro steps in the dissipative branch shows that a finite Josephson coupling exists in the dissipative state. Although the nanobridge is heated, our model shows that the temperature remains below the critical temperature. This work provides evidence that Josephson behavior can still exist in thermally hysteretic weak-link devices and will allow extension of the temperature range over which nanobridge-based single-flux-quantum circuits, micron-sized superconducting quantum interference devices (i.e., nanoSQUIDs), and Josephson voltage standards can be used.

DOI
10.1103/physrevapplied.13.024070

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We present measurements of microwave-induced Shapiro steps in a superconducting nanobridge weak link in the dissipative branch of a hysteretic current-voltage characteristic. We demonstrate that Shapiro steps can be used to infer a reduced critical current and an associated local temperature. Our observation of Shapiro steps in the dissipative branch shows that a finite Josephson coupling exists in the dissipative state. Although the nanobridge is heated, our model shows that the temperature remains below the critical temperature. This work provides evidence that Josephson behavior can still exist in thermally hysteretic weak-link devices and will allow extension of the temperature range over which nanobridge-based single-flux-quantum circuits, micron-sized superconducting quantum interference devices (i.e., nanoSQUIDs), and Josephson voltage standards can be used.
The quantum phase-coherent behavior of superconducting weak links (WLs) is often quenched in the finite voltage state, due to the heat dissipation and related thermal hysteresis. The latter can be reduced by improving heat evacuation and/or by lowering the critical current so a phase-dynamic regime is obtained, albeit over a narrow bias-current and temperature range. Here we demonstrate that an inductive shunt with well-chosen parameters introduces unexpected nonlinear dynamics that destabilize an otherwise stable fixed point in the dissipative branch. This leads to a nonhysteretic behavior with large voltage oscillations in intrinsically hysteretic WL-based micron-size superconducting quantum interference devices. A dynamic thermal model quantitatively describes our observations and further allows us to elaborate on the optimal shunting conditions.
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.
We demonstrate the role of the proximity effect in the thermal hysteresis of superconducting constrictions. From the analysis of successive thermal instabilities in the transport characteristics of micron-size superconducting quantum interference devices with a well-controlled geometry, we obtain a complete picture of the different thermal regimes. These determine whether or not the junctions are hysteretic. Below the superconductor critical temperature, the critical current switches from a classical weak-link behavior to one driven by the proximity effect. The associated small amplitude of the critical current makes it robust with respect to the heat generation by phase slips, leading to a nonhysteretic behavior.
This paper investigates the feasibility of using weak link nanobridges as Josephson junction elements for the purpose of creating Josephson circuits. We demonstrate the development of a single-step electron beam lithography procedure to fabricate niobium nanobridges with dimensions down to . The single-step process facilitates fabrication that is scalable to complex circuits that require many junctions. We measure the IV -characteristics (IVC) of the nanobridges between temperatures of and and find agreement with numerical simulations and the analytical resistively shunted junction (RSJ) model. Furthermore, we investigate the behaviour of the nanobridges under rf irradiation and observe the characteristic microwave-induced Shapiro steps. Our simulated IVC under rf irradiation using both the RSJ model and circuit simulator JSIM are in agreement with the experimental data. As a potential use of nanobridges in circuits requiring many junctions, we investigate the theoretical performance of a nanobridge-based Josephson comparator circuit using JSIM .
We have fabricated and characterized niobium film based superconducting weak link (WL) devices and micron-size superconducting quantum interference devices (µ-SQUIDs) with superconducting WLs as Josephson Junctions. Here we discuss the effect of WL width on the hysteresis and crossover temperature (Th) while keeping the other dimensions fixed. We find that the critical current reduces linearly with the width and thus Th reduces with decreasing width. This makes some of the devices non-hysteretic down to 1.3K. We also discuss the observed excess current in the current-voltage characteristics of these devices, in terms of Andreev reflection.
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.