Reversible ratchet effects in a narrow superconducting ring

Ji Jiang, Yong-Lei Wang, M. V. Milošević, Zhi-Li Xiao, F. M. Peeters, and Qing-Hu Chen

Phys. Rev. B 103, 014502 – Published 5 January 2021

Abstract

We study the ratchet effect in a narrow pinning-free superconductive ring based on time-dependent Ginzburg-Landau (TDGL) equations. Voltage responses to external dc and ac currents at various magnetic fields are studied. Due to asymmetric barriers for flux penetration and flux exit in the ring-shaped superconductor, the critical current above which the flux-flow state is reached, as well as the critical current for the transition to the normal state, are different for the two directions of applied current. These effects cooperatively cause ratchet signal reversal at high magnetic fields, which has not been reported to date in a pinning-free system. The ratchet signal found here is larger than those induced by asymmetric pinning potentials. Our results also demonstrate the feasibility of using mesoscopic superconductors to employ a superconducting diode effect in versatile superconducting devices.

Received 9 November 2020
Accepted 16 December 2020

DOI:https://doi.org/10.1103/PhysRevB.103.014502

Physics Subject Headings (PhySH)

Superconductivity Vortex flows Vortices in superconductors

Thin films Type-II superconductors

Landau-Ginzburg theory Time-dependent Ginzburg-Landau theory

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Ji Jiang ^1,2, Yong-Lei Wang³, M. V. Milošević⁴, Zhi-Li Xiao^5,6, F. M. Peeters⁴, and Qing-Hu Chen ^1,2

¹Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, China
²Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093, China
³Research Institute of Superconductor Electronics, School of Electronic Science and Engineering, Nanjing University, Nanjing 210093, China
⁴Department of Physics, University of Antwerp, 2020 Antwerpen, Belgium
⁵Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
⁶Department of Physics, Northern Illinois University, DeKalb, Illinois 60115, USA

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Vol. 103, Iss. 1 — 1 January 2021

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Images

Figure 1
Schematic view of a narrow, pinning-free superconducting ring with the outer radii $r_{out}$ and the inner radii $r_{in}$ . The thickness of the sample $d$ is assumed to be much smaller than the penetration length $d ≪ λ$ . A perpendicular magnetic field $H$ is applied. A clockwise (counter-clockwise) current is denoted by $+ I$ ( $- I$ ).
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Figure 2
(a) Phase diagram of ratchet voltage signals $V^{R} = V^{+} - V^{-}$ in the current and field parametric range. The phase with negative signals (pink) is present at high currents or low fields, and the phase with positive signals (blue) appears at low currents and high fields. The thick red line represents the transition line to the normal state driven by the counter-clockwise currents. The lowest boundaries of the negative (left) and positive (right) ratchet signals are corresponding to the critical current lines for counter-clockwise and clockwise currents, respectively. Lower panels show voltages and their differences as a function of external dc current of two directions at magnetic fields $H = 0.035 H_{c 2}$ (b), $0.055 H_{c 2}$ (c), and $0.065 H_{c 2}$ (d), where the dashed lines stand for the voltage in the normal state. The voltage unit is $V_{0} = I_{0} / σ$ . As a criterion for critical current, we take the onset of voltage above $10^{- 5} V_{0}$ .
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Figure 3
(a) Potential energy $E_{v p}$ of a single vortex inside the narrow superconducting circular strip as a function of its radial position $r$ at various magnetic field $H$ in the absence of external current. Lower panels show the potential energy with the applied current $| I | = 0.002$ at the magnetic field $H = 0.055 H_{c 2}$ in (b) and $H = 0.065 H_{c 2}$ in (c), i.e., in the vicinity of the critical currents in Figs. 2 and 2, respectively.
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Figure 4
Mean dc voltage as a function of the amplitude of the applied ac current at various magnetic fields (a), and at various frequencies (b). $I_{ac}$ is the amplitude of the applied ac current with a fixed frequency $f = 60$ MHz. A, B, and C mark three prominent negative signal peaks at $H = 0.050$ , 0.060, and $0.065 H_{c 2}$ , respectively. The magnetic field for (b) is kept fixed at $H = 0.065 H_{c 2}$ .
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Figure 5
Snapshots for the evolution of the Cooper-pair density ${| ψ |}^{2}$ . Images in rows A, B, and C present, respectively, ${| ψ |}^{2}$ at peak points A, B, and C in Fig. 4 at $t_{1} = 0$ , $t_{2} = 0.3 P$ , $t_{3} = 0.5 P$ , and $t_{4} = 0.8 P$ within one period.
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Figure 6
Mean dc voltage as a function of the amplitude of applied ac current at various magnetic fields for a superconducting ring with larger width. The frequency of the applied current was kept fixed at $f = 60$ MHz.
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