Long-Range Propagation and Interference of $d$-Wave Superconducting Pairs in Graphene

Long-Range Propagation and Interference of $d$ -Wave Superconducting Pairs in Graphene

D. Perconte, K. Seurre, V. Humbert, C. Ulysse, A. Sander, J. Trastoy, V. Zatko, F. Godel, P. R. Kidambi, S. Hofmann, X. P. Zhang, D. Bercioux, F. S. Bergeret, B. Dlubak, P. Seneor, and Javier E. Villegas

Phys. Rev. Lett. 125, 087002 – Published 18 August 2020

Abstract

Recent experiments have shown that proximity with high-temperature superconductors induces unconventional superconducting correlations in graphene. Here, we demonstrate that those correlations propagate hundreds of nanometers, allowing for the unique observation of $d$ -wave Andreev-pair interferences in ${YBa}_{2} {Cu}_{3} O_{7}$ -graphene devices that behave as a Fabry-Perot cavity. The interferences show as a series of pronounced conductance oscillations analogous to those originally predicted by de Gennes–Saint-James for conventional metal-superconductor junctions. The present demonstration is pivotal to the study of exotic directional effects expected for nodal superconductivity in Dirac materials.

Received 24 February 2020
Revised 22 June 2020
Accepted 22 July 2020

DOI:https://doi.org/10.1103/PhysRevLett.125.087002

Physics Subject Headings (PhySH)

Andreev reflection Proximity effect Quantum interference effects Superconducting order parameter Superconducting phase transition

Cuprates Graphene

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

D. Perconte^1,2, K. Seurre ¹, V. Humbert¹, C. Ulysse³, A. Sander¹, J. Trastoy¹, V. Zatko ¹, F. Godel ¹, P. R. Kidambi^4,5, S. Hofmann⁵, X. P. Zhang^6,7, D. Bercioux ^7,8, F. S. Bergeret ^6,7, B. Dlubak ¹, P. Seneor¹, and Javier E. Villegas^1,*

¹Unité Mixte de Physique, CNRS, Thales, Université Paris-Saclay, 91767 Palaiseau, France
²Laboratorio de Bajas Temperaturas y Altos Campos Magnéticos, Departamento de Física de la Materia Condensada, Instituto Nicolás Cabrera and Condensed Matter Physics Center (IFIMAC), Universidad Autónoma de Madrid, E-28049 Madrid, Spain
³Centre for Nanoscience and Nanotechnology, CNRS, Université Paris-Sud/Université Paris-Saclay, Boulevard Thomas Gobert, 91120 Palaiseau, France
⁴Department of Chemical and Biomolecular Engineering, Vanderbilt University, 2400 Highland Avenue, Nashville, Tennessee 37212, USA
⁵Department of Engineering, University of Cambridge, Cambridge CB3 0FA, United Kingdom
⁶Centro de Fisica de Materiales (CFM-MPC), Centro Mixto CSIC-UPV/EHU, 20018 Donostia-San Sebastián, Basque Country, Spain
⁷Donostia International Physics Center (DIPC), Manuel de Lardizabal, 4, 20018 Donostia-San Sebastián, Spain
⁸IKERBASQUE, Basque Foundation of Science, 48011 Bilbao, Basque Country, Spain

^*javier.villegas@cnrs-thales.fr

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Issue

Vol. 125, Iss. 8 — 21 August 2020

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Images

Figure 1
Interferences in a proximitized cavity (a) An electron Andreev reflected at the SC-cavity interface propagates as a hole back to the other end, where it is normal reflected toward the SC-cavity interface to undergo again Andreev reflection (AR). The lower AR is the time reversal process of the upper one. (b) The electron can also be normal reflected at the SC cavity, travel back to the other cavity interface to be again normal reflected. This process results in Fabry-Perot resonances.
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Figure 2
(a),(b) Micrograph of a graphene-YBCO superconducting device. The scale bar is $10 μ m$ . (a) shows a zoom on the junction: Superconducting electrodes (SC) are connected by graphene bridges ( $G$ ) on top of insulating YBCO (INS). The scale bar is $100 μ m$ . (c) Micrograph of a device with the top gate. (d) Scheme of the graphene homojunction model. The doping depends on whether graphene lies on insulating or superconducting YBCO, which results in three graphene regions $A$ , $B$ , $C$ with different Fermi energy. This creates the cavity where interferences occur. The lower scheme shows the equivalent electrical circuit. The YBCO-Au-graphene interface, characterized by a barrier strength $Z$ , is measured in series with the cavity.
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Figure 3
(a),(d) Conductance versus $V_{bias}$ for two different devices, $B 3 U$ (a) and $B 4 U$ (b) measured at 3.2 K. Vertical lines point out the series of oscillations, and the horizontal double-headed arrows indicate the periods $V_{long}$ (black) and $V_{short}$ (red). The shaded area indicates the width $2 δ$ of the superconducting-gap related feature. (b) and (e) show corresponding full-model calculations of the conductance with the $Z$ and $α$ indicated in the legend (c) and (f) shows simulations for a proximitized graphene cavity alone, without finite- $Z$ junction in series.
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Figure 4
(a) Conductance versus $V_{bias}$ for device $A 5 U$ , measured at $T = 4 K$ . (b) Same device conductance (color scale) as function of bias voltage (horizontal axis) and gate voltage (vertical axis). (c) Full-model calculation of the conductance with $Z$ and $α$ indicated in the legend (d). Corresponding full-model calculation of the conductance as a function of bias and the Fermi energy variation in the cavity.
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Figure 5
Oscillations’ period as a function of the cavity length $L_{device}$ . The black and red dashed lines respectively correspond to the period theoretically expected for electron (Fabry-Perot) and Andreev-pair (de Gennes–Saint-James) interferences.
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