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Philosophical Magazine B

Shapiro steps in superconducting films with a periodic pinning potential

Lieve Van Look, Erik Rosseel, Margriet J. Van Bael, Y. Bruynseraede, V. V. Moshchalkov

Published May 1, 2000• 0 citations
Publisher

Abstract

Shapiro voltage steps at voltages V n = nV 0 occur in the voltage-current characteristics of a superconducting film with a periodic pinning potential in the presence of rf radiation. We report on their experimental observation in a superconducting film with a square lattice of perforated microholes (antidots) and on numerical simulations showing the Shapiro steps in the voltage-current characteristics of the dc flux transformer. For the square antidot lattice, the ratio VQ/V of the step height to the applied rf frequency depends on the antidot lattice period d, while in the flux transformer geometry this ratio can be tuned by the magnetic field. This tuneability of the resolution makes the flux transformer a good candidate for applications (e.g. broad-band radiation detection).

DOI
10.1080/01418630008221950

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Shapiro voltage steps at voltages V n = nV 0 occur in the voltage-current characteristics of a superconducting film with a periodic pinning potential in the presence of rf radiation. We report on their experimental observation in a superconducting film with a square lattice of perforated microholes (antidots) and on numerical simulations showing the Shapiro steps in the voltage-current characteristics of the dc flux transformer. For the square antidot lattice, the ratio VQ/V of the step height to the applied rf frequency depends on the antidot lattice period d, while in the flux transformer geometry this ratio can be tuned by the magnetic field. This tuneability of the resolution makes the flux transformer a good candidate for applications (e.g. broad-band radiation detection).
Shapiro steps in an RF-field-driven dc-SQUID (RFDS), where an RF signal is coupled to the SQUID loop magnetically, are numerically investigated. We calculate the current–voltage characteristics of RFDSs under no dc offset flux, which show the enhancement of the even-order Shapiro steps. First, the maximum second (the lowest even-order) step height is evaluated as a function of the normalized frequency Ω. In the case of the inductance parameter βL ≥ 1.0, the maximum second step height is maintained at a certain value in the low frequency region. In the case of βL < 1.0, on the other hand, the maximum step height decreases in the low frequency region of Ω < 0.10. The dependence of the current positions of the step upon the RF signal amplitude shows that the voltage transition at the non-superconductive area between the superconducting interference lobes limits the upper current position of the step.
We have studied in detail the current-voltage (I-V) curves of dc SQUIDs in the presence of rf fields in the frequency range 2–18 GHz. Strong voltage locking at half-integral as well as the usual integral Shapiro step spacing is observed when the applied dc-magnetic flux is close to half-integral numbers of flux quanta. Numerical simulations are in excellent agreement with the experimental I-V curves. The half-integral steps are found to be associated with the flip-flop between two adjacent fluxoid states of the SQUID synchronized to the rf field.
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)(VI)(VI) characteristic. The effect exists at low RF power and at frequencies fff approximately ten times smaller than ${f}_{0}={I}_{c}{R}_{N}/{\mathrm{\ensuremath{\Phi}}}_{0}$ (where Ic{I}_{c}Ic​ is the critical current, RN{R}_{N}RN​ 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 Rdiff=dV/dI{R}_{\mathrm{diff}}=dV/dIRdiff​=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 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 demonstrate a zero-crossing Shapiro step in a three-junction SQUID (3J-SQUID) coupled with two phase-shifted RF signals. The operation is based on periodic flux quantum transitions in the 3J-SQUID under the zero- and negatively-biasing conditions. A test circuit is fabricated using a Nb/AlO/sub x//Nb junction technology. When we feed RF signals up to 10.5 GHz, we observe a Shapiro step crossing the zero-current axis at the voltage position of the 1st order. The experimental current-voltage characteristics are quantitatively reproduced by simulation. Zero-crossing conditions for the DC offset flux and the RF power are obtained experimentally, which is also confirmed by simulation. A programmable Josephson voltage standard is discussed as one of the possible applications.
We study the current-voltage characteristics of a superconducting Wheatstone bridge in the presence of radio frequency current sources. Besides the regular integer Shapiro steps in the current-voltage characteristics observed when the voltage is measured between the input and output leads of the dc biasing current, we also found additional integer steps in the transverse voltage for large value of the dc biasing current. An explanation for these steps is given in terms of competing circulating currents in the bridge.