Parametric amplification of vortex-antivortex pair generation in a Josephson junction

G. R. Berdiyorov, M. V. Milošević, S. Savel'ev, F. Kusmartsev, and F. M. Peeters

Phys. Rev. B 90, 134505 – Published 6 October 2014

Abstract

Using advanced three-dimensional simulations, we show that an Abrikosov vortex, trapped inside a cavity perpendicular to an artificial Josephson junction, can serve as a very efficient source for generation of Josephson vortex-antivortex pairs in the presence of the applied electric current. In such a case, the nucleation rate of the pairs can be tuned in a broad range by an out-of-plane ac magnetic field in a broad range of frequencies. This parametrically amplified vortex-antivortex nucleation can be considered as a macroscopic analog of the dynamic Casimir effect, where fluxon pairs mimic the photons and the ac magnetic field plays the role of the oscillating mirrors. The emerging vortex pairs in our system can be detected by the pronounced features in the measured voltage characteristics, or through the emitted electromagnetic radiation, and exhibit resonant dynamics with respect to the frequency of the applied magnetic field. Reported tunability of the Josephson oscillations can be useful for developing high-frequency emission devices.

Received 2 July 2013
Revised 23 December 2013

DOI:https://doi.org/10.1103/PhysRevB.90.134505

Authors & Affiliations

G. R. Berdiyorov^1,2, M. V. Milošević³, S. Savel'ev¹, F. Kusmartsev¹, and F. M. Peeters^3,*

¹Department of Physics, Loughborough University, Leicestershire, LE11 3TU, United Kingdom
²Qatar Environment and Energy Research Institute, Doha, Qatar
³Departement Fysica, Universiteit Antwerpen, Groenenborgerlaan 171, B-2020 Antwerpen, Belgium

^*francois.peeters@untwerpen.be

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Vol. 90, Iss. 13 — 1 October 2014

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Images

Figure 1
Oblique view of the system: two superconducting layers (of thickness $d ≪ λ)$ with a normal metal junction (of thickness $s ≪ ξ, λ)$ in between, and external current $I$ and magnetic field $H$ applied perpendicularly to the junction plane. The shown hole of radius $R$ is designed to trap Abrikosov vortices.
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Figure 2
Time-averaged voltage vs applied current density $(I - V)$ characteristics of the sample without (solid circles) and with (open symbols) an Abrikosov vortex trapped in the hole of radius $R = 1.6 ξ$ . The length of the sample is $L = 100 ξ$ , the thickness of the superconducting layers is $d = 5 ξ$ , and the thickness of the normal layer is $s = 0.4 ξ$ . The out-of-plain magnetic field $H$ is applied either in the positive (open squares) or the negative (open triangles) direction. The inset shows the field dependence of the critical current $j_{c}$ .
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Figure 3
(a) Voltage vs time characteristics $[V (t)]$ of the sample with dimensions $L = 100 ξ$ , $w = 20 ξ$ , $d = 5 ξ$ , $s = 0.4 ξ$ , and $R = 1.6 ξ$ , in the presence of a trapped Abrikosov vortex, for $j > j_{c}$ (fixed at $j = 0.067 j_{0})$ , and three values of the magnetic field $H$ . Voltage is measured in $V_{0} = c Φ_{0} ρ_{n} / 8 π^{2} λ ξ$ , current density in $j_{0} = c Φ_{0} / 8 π^{2} λ^{2} ξ$ , and time in $t_{GL} = 4 π λ^{2} / c^{2} ρ_{n}$ $(ρ_{n}$ is the normal-state resistivity). (b) Characteristic crossing time of a Josephson fluxon over half the length of the sample, $δ t$ , as a function of $H$ . (c) Period of the voltage oscillations $Δ t$ as a function of $H$ . Panels 1, 2a, and 3 show isosurface plots of the Cooper-pair density (isovalue is 10% of ${| ψ |}_{\max}^{2})$ for $H = 0$ at times indicated on the $V (t)$ curve. Panel 2b shows the contour plot of the phase of the order parameter at the surface of the sample at time indicated by point 2. White circles indicate the position of the vortices and arrows indicate the direction of motion of Josephson V-Av pairs.
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Figure 4
(a) Number of Josephson V-Av pairs generated per unit time, $n$ , as a function of the frequency of the oscillating magnetic field $H = H_{dc} + H_{ac} sin (2 π ν t)$ for $H_{dc} = - 0.0025 H_{c 2}$ . The current $j = 0.066 j_{0} = 0.99 j_{c}$ and the ac field component is $H_{ac} = 0.0025 H_{c 2}$ . The sample parameters are the same as those in Fig. 3. The insets show the enlargement of the lower frequency part of the $n (ν)$ curve. (b–d) $V (t)$ curves of the sample for the frequencies of the magnetic field indicated in panel (a) by points 1–3, respectively. Dashed curves show the profile of the ac magnetic field in arbitrary units.
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Figure 5
(a) $n (ν)$ characteristics of the sample at $j = 1.01 j_{c}$ for $H_{dc} = - 0.0025 H_{c 2}$ and $H_{ac} = 0.0025 H_{c 2}$ (cf. Fig. 4). (b, c) $V (t)$ characteristics of the sample for the frequency of the magnetic field indicated in panel (a) by points 1 and 2, respectively. Dashed/red curves show the profile of the ac magnetic field in arbitrary units.
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Figure 6
Fourier power spectrum of the voltage for four different values of the frequency of the ac magnetic field $H / H_{c 2} = - 0.0025 + 0.0025 sin (2 π ν t)$ , as indicated by vertical dashed lines.
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