Phase Asymmetry of Andreev Spectra from Cooper-Pair Momentum

Abhishek Banerjee, Max Geier, Md Ahnaf Rahman, Candice Thomas, Tian Wang, Michael J. Manfra, Karsten Flensberg, and Charles M. Marcus

Phys. Rev. Lett. 131, 196301 – Published 9 November 2023

Abstract

In analogy to conventional semiconductor diodes, the Josephson diode exhibits superconducting properties that are asymmetric in applied bias. The effect has been investigated in a number of systems recently, and requires a combination of broken time-reversal and inversion symmetries. We demonstrate a dual of the usual Josephson diode effect, a nonreciprocal response of Andreev bound states to a superconducting phase difference across the normal region of a superconductor-normal-superconductor Josephson junction, fabricated using an epitaxial $InAs / Al$ heterostructure. Phase asymmetry of the subgap Andreev spectrum is absent in the absence of in-plane magnetic field and reaches a maximum at 0.15 T applied in the plane of the junction transverse to the current direction. We interpret the phase diode effect in this system as resulting from finite-momentum Cooper pairing due to orbital coupling to the in-plane magnetic field. At higher magnetic fields, we observe a sign reversal of the diode effect that appears together with a reopening of the spectral gap. Within our model, the sign reversal of the diode effect at higher fields is correlated with a topological phase transition that requires Zeeman and spin-orbit interactions in addition to orbital coupling.

Received 4 January 2023
Revised 10 August 2023
Accepted 16 October 2023

DOI:https://doi.org/10.1103/PhysRevLett.131.196301

Physics Subject Headings (PhySH)

Proximity effect

Diodes Josephson junctions

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Abhishek Banerjee¹, Max Geier ¹, Md Ahnaf Rahman ¹, Candice Thomas ², Tian Wang², Michael J. Manfra^2,3, Karsten Flensberg ¹, and Charles M. Marcus ¹

¹Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark
²Department of Physics and Astronomy, and Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907, USA
³School of Materials Engineering, and School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, USA

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Vol. 131, Iss. 19 — 10 November 2023

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Images

Figure 1
Device schematic and micrograph. (a) Schematic of a planar Josephson junction device consisting of two superconducting leads (blue) of width $w_{s} = 1.8 μ m$ in epitaxial contact with the underlying semiconductor (brown). The normal region between the two leads is of width $w_{n} = 100 nm$ , length $l = 1.6 μ m$ . The 2D electron wave function extends over a nominal thickness of $w_{z} \sim 20 nm$ that includes the width of the InAs quantum well and the two insulating ${In}_{0.75} {Ga}_{0.25} As$ barriers. (b) Cross section of the device depicted schematically showing various layers comprising the heterostructure stack. Al (7 nm) is epitaxially grown on an ${In}_{0.75} {Ga}_{0.25} As (10 nm) / InAs (7 nm) / {In}_{0.75} {Ga}_{0.25} As (4 nm)$ quantum well. Meandering perforations in the Al leads help with hardening of the superconducting gap. (c) False-colored electron micrograph of a planar Josephson junction device measured in a three-terminal configuration. dc biases, $V_{T}$ and $V_{B}$ , are applied to the top and bottom ohmics through current amplifiers connected to the respective terminals. The superconducting loop is grounded. An out-of-plane magnetic field $B_{⊥}$ threads magnetic flux through the superconducting loop for phase biasing. In-plane magnetic field $B_{∥}$ is applied in the plane of the device parallel to the S-N interfaces.
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Figure 2
Andreev bound state spectrum. (a) Differential conductance measured in Device 1 as a function of $B_{⊥}$ at different value of $B_{∥}$ . At $B_{∥} = 0$ , the Andreev bound state spectrum is phase-symmetric within each flux lobe. (b) For nonzero $B_{∥}$ , the spectrum acquires an asymmetry within each flux lobe. (c) At a critical magnetic field $B_{c} = B_{∥} = 0.22 T$ , the asymmetry disappears. (d),(e) At higher magnetic field ( $B_{∥} > B_{c}$ ), the asymmetry reappears with an opposite sense and eventually disappears for an even higher field. (f)–(h) The sense of asymmetry within each flux lobe is opposite for $B_{∥} = + 0.14 T$ and (h) $B_{∥} = - 0.14 T$ . There is no asymmetry at (g) $B_{∥} = 0$ . Top gate voltage $V_{1} = 86 mV$ .
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Figure 3
In-plane field dependence. (a) Diode efficiency $η^{*}$ estimated from the phase-dependent tunneling spectra. (b) Differential conductance measured as a function of $B_{∥}$ at the center of the flux lobe, corresponding to $ϕ = 0$ at $B_{∥} = 0$ . $B_{c} ≃ 220 mT$ is the critical field at which the spectral gap closes. At the same field, we observe that $η^{*}$ changes sign. Top gate voltage $V_{1} = 86 mV$ same as in Fig. 2. (c) $η^{*}$ and (d) differential conductance spectrum at a top gate voltage setting ( $V_{1} = 65 mV$ ) where the gap-reopening signature is present without ZBCPs. The field range where $η^{*} < 0$ appears to be correlated with the reopening of the spectral gap in both cases.
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Figure 4
Model and numerical results. (a) Sketch of the Josephson junction cross section formed by two superconducting films of width $w_{s} = 400 nm$ and separation $w_{n} = 100 nm$ deposited on top of a 2DEG with wave function profile $| Ψ |^{2}$ (sketch). The mean separation between the 2DEG and the superconductor is $d \sim 15 nm$ . Cooper pairs in the proximitized 2DEG acquire a finite momentum $q = π B_{∥} d / Φ_{0}$ from the flux $Φ = B_{∥} d Δ y$ enclosed by electron hopping between the layers at different positions $Δ y$ . (b) Calculated DOS with in-plane field $B_{∥} = - 160$ , 0, 160, 210, 240, and 300 mT (from top left to bottom right) with loop inductance $L = 1 nH$ and a Gaussian linewidth of $30 μ eV$ . (c) Critical current diode efficiency $η$ . (d) DOS at equilibrium phase $ϕ_{0}$ .
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