DIRECT OBSERVATION OF JOSEPHSON VORTICES Young Scientist Contest 2016 of the Belgian Physical Society DIRECT OBSERVATION OF JOSEPHSON VORTICES presented by Lise SERRIER-GARCIA Lise SERRIER-GARCIA, Tristan CREN, Dimitri RODITCHEV, François DEBONTRIDDER, Christophe BRUN, Juan Carlos CUEVAS, Vagner H. L. BESSA, Milorad MILOŠEVIĆ Institute for Nanoscale Physics and Chemistry, Leuven, Belgium Institut des Nanosciences de Paris, CNRS-UPMC, Paris, France, Departamento de Física Teórica de la Materia Condensada, Universidad Autónoma de Madrid, SPAIN Departement Fysica, Universiteit Antwerpen, BELGIUM

The supercurrent is zero at each step of quantum flux. JOSEPHSON EFFECT 𝐼 𝑚𝑎𝑥 𝐼 𝑐 superconductor tunneling barrier Superconducting Quantum Interference Device (SQUID) A very sensitive sensor of extremely subtle magnetic fields magnetic field 𝐼 𝑚𝑎𝑥 𝐼 𝑐 = sin Δ𝜑 =sin⁡( 𝜙 𝜙 0 ) magnetic flux: 𝜙= 𝐵 𝑆 quantum flux: 𝜙 0 = ℎ 2𝑒 The supercurrent is zero at each step of quantum flux. 2

SUPERCONDUCTING ELECTRODES Si Pb 𝑏𝑎𝑖𝑠 𝑣𝑜𝑙𝑡𝑎𝑔𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 STM Non-superconducting metal Superconductor Insulator 𝐶∝ 𝜌 𝑛 𝑒𝑉 ℜ𝑒 𝑒𝑉 𝑒𝑉 2 − ∆ 2 at T = 0 normalized conductance 𝑇=0.3 𝐾 𝑇 𝑐 =7 𝐾 Bias voltage (mV) Using scanning tunneling spectroscopy, we directly access to the local electronic density of states. 3

NANOSTRUCTURES CONTROLLED BY PREPARATION CONDITIONS 1 x 1 µm² 2 x 2 µm² 1 x 1 µm² J. Phys. Chem C 119 12651 (2015) The lead on silicon growth follows a self-organisation. Temperature, pressure, quality and amount of lead determine the nanostructures. 4

BUILDING A JOSEPHSON JUNCTION 𝜉 𝑛 ≈15 𝑛𝑚 nanostructure What? 4 𝜉 𝑛 ≈15 𝑛𝑚 thickness (nm) topography conductance nanostructure Phys Rev Lett 110 157003 (2013) Bias voltage (mV) Superconductivity is not limited to the nanostructures. 5

JOSEPHSON JUNCTION The distance is reduced to few tens of nanometer superconductor d≈45 𝑛𝑚 Josephson junction 1 conductance conductance conductance map superconductor Bias voltage (mV) The distance is reduced to few tens of nanometer creating a Josephson junction. 6

JOSEPHSON JUNCTIONS WITH MAGNETIC FIELD non-supercodnucting metal superconductors magnetic field 1 x 1 µm² 5 thickness (nm) topography Array of Josephson junctions. 7

ABRIKOSOV AND JOSEPSHON VORTICES Nat Phys 11 332-337 (2015) 1 x 1 µm2 magnetic field 0 mT 180 mT 60 mT 120 mT 1 conductance 8

THE GINZBURG-LANDAU EQUATIONS Minimizing the free energy of the Ginzburg-Landau theory… 𝑓 𝑟 =𝑎 𝛹(𝑟) 2 + 𝑏 2 𝛹(𝑟) 4 + 1 2 𝑚 ∗ ℏ 𝑖 𝛻−2𝑒 𝐴 𝑟 𝛹 𝑟 + µ 0 2 𝐵 𝑟 2 Condensation Kinetic Magnetic Phys Rev E 86 056709 (2012) Nat Phys 11 332-337 (2015) Phys Rev B 65 104515 (2002) 𝐻 Current 𝑗 𝑟 Phase 𝜑 𝑟 Amplitude |Ψ 𝑟 | … to simulate the Abrikosov vortices. 9

SIMULATING THE SUPERCONDUCTORS… Abrikosov vortex Josephson junction 500 x 500 nm2 H = 120 mT Nat Phys 11 332-337 (2015) 1 2π amplitude |ψ| phase ϕ Ginzburg-Landau equations describe the superconductivity in the nanostructures but not in the Josephson junctions. 10

… SIMULATING THE JOSEPHSON EFFECT… Phase ϕ Interference pattern J Superconductor 1 Josephson junction Superconductor ∆𝜑 𝑖𝑛𝑣 =𝜑 𝑟 𝑎 −𝜑 𝑟 𝑏 − 2𝑒 ħ 𝑟 𝑏 𝑟 𝑎 𝐴 . 𝑑𝑙 𝐽 𝒓 = 𝜓 0 𝑒 − 𝒓− 𝒓 𝒂 2 𝜉 𝑛 2 + 𝜓 0 𝑒 − 𝒓− 𝒓 𝑏 2 𝜉 𝑛 2 + 2 𝜓 0 2 sin ∆𝜑 𝑖𝑛𝑣 𝒓 + 𝜑 0 11

Simulations and experiments are in very good agreement. … TO SIMULATE THE JOSEPSHON VORTICES Josephson vortex 500 x 500 nm2 H = 120 mT Nat Phys 11 332-337 (2015) 1 1 superconductivity conductance Simulations and experiments are in very good agreement. 12

JOSEPSHON VORTICES IN ELECTRONIC CIRCUITS Nat Phys 11 332-337 (2015) 𝐼 1 𝐼 2 𝐼 Josephson vortices can be induced by supercurrents instead of magnetic field. 13

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JOSEPSHON VORTICES AS REAL VORTICES? 1 1 Currents Superconducting correlations 𝑐 𝒅𝒍 𝑱= 𝑒 ∗ 𝑚 ∗ 𝑐 𝒅𝒍 𝛹 𝒓 2 ħ𝛁𝜑 𝒓 − 𝑒 ∗ 𝑨 𝒓 𝟎 = ħ 𝐿 2𝜋 − 2𝑒 𝐵𝑆 ⇔ 𝐵𝑆=𝐿 𝛷 0 a Josephson vortex corresponds to a quanta of magnetic flux.

Josephson vortex cores have a normal state. AN ELECTRONIC DENSITY OF STATES! superconductor Josephson junction normal layer Abrikosov vortex Josephson vortex x x x x x Josephson vortex cores have a normal state.

ABRIKOSOV VORTICES supercurrents vortex core magnetic field vortices in superconductors An Abrikosov vortex has: a normal core, supercurrents around it, one quantum of magnetic flux.