Measurements of Phase Dynamics in Planar Josephson Junctions and SQUIDs

Open Access

Measurements of Phase Dynamics in Planar Josephson Junctions and SQUIDs

D. Z. Haxell, E. Cheah, F. Křížek, R. Schott, M. F. Ritter, M. Hinderling, W. Belzig, C. Bruder, W. Wegscheider, H. Riel, and F. Nichele

Phys. Rev. Lett. 130, 087002 – Published 23 February 2023

Abstract

We experimentally investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial $InAs / Al$ heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature $T^{*}$ is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, $T^{*}$ is also tuned by a magnetic flux.

Received 12 April 2022
Revised 15 September 2022
Accepted 19 January 2023

DOI:https://doi.org/10.1103/PhysRevLett.130.087002

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Andreev reflection Critical current Josephson effect Phase slips Proximity effect

Josephson junctions Layered semiconductors Superconducting devices Two-dimensional electron system

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

D. Z. Haxell¹, E. Cheah ², F. Křížek ^1,2, R. Schott ², M. F. Ritter¹, M. Hinderling¹, W. Belzig ³, C. Bruder⁴, W. Wegscheider², H. Riel¹, and F. Nichele^1,*

¹IBM Research Europe—Zurich, Säumerstrasse 4, 8803 Rüschlikon, Switzerland
²Solid State Physics Laboratory, ETH Zurich, 8093 Zurich, Switzerland
³Fachbereich Physik, Universität Konstanz, D-78457 Konstanz, Germany
⁴Department of Physics, University of Basel, Klingelbergstrasse 82, CH-4056 Basel, Switzerland

^*fni@zurich.ibm.com

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Issue

Vol. 130, Iss. 8 — 24 February 2023

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Images

Figure 1
(a) False-colored electron micrograph of the device under study and measurement configuration. The InAs is highlighted in pink and the Al in blue. Gates are drawn on the image and highlighted in yellow. (b) Differential resistance $R$ as a function of $B_{⊥}$ and $I_{DC}$ obtained with $V_{G 1} = - 180 mV$ and $V_{G 2} = - 140 mV$ . The amplitude of the switching current oscillations, $Δ I$ , is marked. (c) Differential resistance of JJ1 in isolation, with $V_{G 1} = - 180 mV$ and $V_{G 2} = - 450 mV$ . Large fluctuations close to $B_{⊥} = 0$ are marked with an arrow. (d) Differential resistance of JJ2 in isolation, with $V_{G 1} = - 550 mV$ and $V_{G 2} = - 140 mV$ . The peak at $B_{⊥} = 0$ is less than half $Δ I / 2$ in (b).
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Figure 2
(a) Switching probability distributions (SPDs) for JJ1 for various temperatures. Colors are defined in (e) and are consistent throughout the text. (b) As in (a), but for JJ2. (c) Escape rate $Γ$ of JJ1, obtained from the data in (a) using Eq. (1). (d) As in (c), but for JJ2. (e) Mean switching current $I_{SW}$ of SPDs for JJ1 as a function of temperature (circles) together with a fit to a Monte Carlo simulation (line). Transition temperature $T^{*}$ is indicated by a vertical line, dividing a regime of MQT (blue shading) and PD. (f) Standard deviation $σ_{1}$ of SPDs for JJ1, as a function of temperature. (g),(h) As in (e) and (f), for JJ2.
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Figure 3
Mean $I_{M, S}$ (a) and standard deviation $σ_{S}$ (b) of the SPDs in the SQUID configuration as a function of $B_{⊥}$ , for temperatures between 20 and 800 mK. (c) Mean switching current of JJ2 as a function of $T$ , derived from the SQUID oscillations (circles) and measured with JJ2 in isolation (squares). The solid line is $Δ I_{M, S} / 2$ obtained from a Monte Carlo simulation fitted to the experimental results. (d) Standard deviation of the SPD in JJ1 measured in isolation (squares) together with the mean of $σ_{S}$ from (b) (circles) as a function of temperature. The solid line is the result of the Monte Carlo simulation presented in (c). (e) SQUID critical current obtained by fitting the SPDs for $T = 20 mK$ to an MQT escape rate. (f) Color map of fitted standard deviation $σ_{S}$ , with transition temperature $T^{*}$ marked by a dashed line.
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Figure 4
(a) Switching currents of JJ2 as a function of $V_{G 2}$ when measured in isolation (squares) and in the SQUID configuration (circles), together with the critical current derived from Monte Carlo simulations (diamonds). (b)–(d) Standard deviation of SPDs measured in the SQUID configuration for three values of $V_{G 1}$ . Blue shading highlights MQT regimes.
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