The Josephson Effect Half-Centennial Symposium University of Cambridge --- June 23, 212 Determining the Order Parameter of Unconventional Superconductors by Josephson Interferometry - - Dale J. Van Harlingen University of Illinois at Urbana-Champaign
My Physics Career --- 197-212 PROJECTS involving the Josephson effect x PROJECTS not involving the Josephson effect Transport in pure metals using SLUGs (with Jim Garland) Thermoelectric effects in superconductors using SQUIDs Quantum Noise and 1/f noise in SQUIDs Josephson junction arrays Non-equilibrium superconductivity using SQUIDs x Scanning tunneling microscopy Scanning SQUID microscopy Vortex imaging Current-phase relations of Josephson junctions (e.g. SFS π-junctions) Josephson interferometry x Stripes in the pseudogap phase Decoherence in superconducting qubits Entanglement in solid state systems Search for Majorana fermions in topological Josephson devices
David Schonberg retirement dinner --- 1978
John Waldram screened room --- 1977
Cavendish Low Temperature Physics Group 1977
My Year in Cambridge --- 1977-1978 NATO Postdoctoral Fellowship First trip outside the USA -- start of many international travels Learned about cricket Learned about the Josephson effect and phase coherence from John Waldram Learned about measuring Current-Phase Relations Did nice experiment on thermoelectric effects in superconductors, precursor to the pairing symmetry experiments Celebrated the Nobel Prize to Neville Mott Met John Clarke Superconductivity was much simpler then.
Conventional ( classic ) superconductivity BCS theory: Bardeen, Cooper, Schrieffer (1957) k' 1 k 2 q e - e - MECHANISM = attractive phonon-mediated electron-electron interaction Cooper pairing k 1 k' 2 GROUND STATE = superfluid pair condensate ψ = n s e iϕ macroscopic phase coherence EXCITATIONS = normal quasiparticles with an isotropic energy gap k z Δ(k) = Δ 23.2K k y Liquid He k x s-wave
Unconventional superconductivity What does unconventional mean? Not BCS Mechanism other than phonon-mediated pairing Symmetry not s-wave exhibits anisotropy in phase and/or magnitude 1st indication: UPt 3 (heavy fermion) two peaks in specific heat 1st confirmation: YBa 2 Cu 3 O 7-x (high-t c superconductor) d-wave Cuprate superconductors: YBa 2 Cu 3 O 7-x T c = 92K d-wave Now, there are many candidates for unconventional superconductivity
Superconductivity timeline cuprates fullerenes conventional heavy fermion
Growing Family of Unconventional Superconductors Cuprate superconductors YBa 2 Cu 3 O 7-x T c = 95K d-wave 115 superconductors CeCoIn 5 T c = 2.3K d-wave Organic superconductors κ-(bedt-ttf) 2 Cu[N(CN) 2 ]Br T c = 11.6K anisotropic d-wave Ruthenate superconductors Sr 2 RuO 4 T c = 1.5K Heavy Fermion superconductors UPt 3 T ca =.5 T cb =.45K p x ip y (k x2 -k y2 ) k z (k x ik y ) 2 k z
EVEN PARITY STATES ODD PARITY STATES PAIRING STATE MAGNITUDE RELATIVE PHASE Δ φ PAIRING STATE MAGNITUDE Δ RELATIVE PHASE φ isotropic s 1 p x 1 π.5 -.5 π 2 anisotropic s d x 2 -y 2 - - d x 2 -y 2 i ε s 9 18 27 36 1.5 9 18 27 36 1.5 9 18 27 36 1 π π 2 9 18 27 36 π 9 18 27 36 9 18 27 36 9 18 27 36. p y - p x i ε p y 1.5 9 18 27 36 1.5 9 18 27 36 θ π π 2 π π 9 18 27 36 9 18 27 36 9 18 27 36 θ.5 π 2 9 18 27 36 9 18 27 36 d x 2 -y 2 i ε d xy 1.5 9 18 27 36 θ π π 9 18 27 36 θ Complex order parameter broken time-reversal symmetry phase shift δ, π
Experimental tests of the symmetry 1. Parity (even = spin-singlet vs. odd = spin-triplet) NMR Knight shift not always definitive 2. Real vs. complex order parameter muon spin resonance senses spontaneous internal magnetic field Kerr effect 3. Magnitude of order parameter (energy gap) (a) thermodynamic, electrodynamic, optical, tunneling,... experiments that count number of excitations (b) spectroscopies that probe the k-space anisotropy 4. Phase of order parameter (a) quasiparticle tunneling spectroscopy --- sensitive to sign change through formation of zero-energy bound states (b) Josephson interferometry --- sensitive to the phase anisotropy
Josephson interferometry: measuring the phase anisotropy the corner SQUID Unconventional SC single crystal Conventional SC thin film loop dc SQUID (Superconducting QUantum Interference Device) measures the phase shift inside the crystal between orthogonal directions Josephson tunnel junctions tunneling selects direction in k-space Wollman, Ginsberg, Leggett, Van Harlingen (1993)
Josephson interferometry measuring the phase shift between different directions δ SC crystal Josephson junctions δ dc SQUID s-wave SC thin film loop single junction δ δ
The corner SQUID experiment s-wave d-wave - - 1. Critical current.8.6.4.2. -3-2 -1 1 2 3 Magnetic flux (Φ ) -3-2 -1 1 2 3 Magnetic flux (Φ ) 8 7 6 corner SQUIDs 1µm Observations 5 4 3 2 edge SQUIDs 1-1. π -.5 π. π.5 π 1. π 1.5 π 2. π Phase shift D. A. Wollman, D. J. Van Harlingen, W. C. Lee, D. M. Ginsberg, and A. J. Leggett, Phys. Rev. Lett. 71, 2134 (1993)
The corner junction experiment Critical current 1..8.6.4.2 s-wave d-wave - -. -6-4 -2 2 4 6 Magnetic flux 6 4 2-2 -4-6 Magnetic flux Critical current ( µ A) 6 4 2-1 -5 5 1 Applied magnetic field (mg) D. A. Wollman, D. J. Van Harlingen, J. Giapintzakis, and D. M. Ginsberg
Grain boundary junctions Geometry for testing symmetry: 45 -asymmetric junction facets sample different signs of the d-wave order parameter Multi-corner junction Maximum I c not at B=O Symmetric with respect to field polarity S-wave would give Fraunhofer pattern H. Hilgenkamp, J. Mannhart, and B. Mayer
The Quest for Complex Superconductors Heavy Fermion superconductors: UPt 3 T ca =.5 T cb =.45K Ruthenate superconductors: Sr 2 RuO 4 T c = 1.5K (k x2 -k y2 ) k z (k x ik y ) 2 k z complex p-wave
Josephson interferometry of complex order parameters Angle SQUID 1. δ Critical current.5 π/4 π/2 3π/4 π δ = phase shift. -1. -.5..5 1. Magnetic flux (Φ/Φ ) 1. Angle junction δ Critical current.8.6.4.2 π/4 π/2 3π/4 π. -3-2 -1 1 2 3 Magnetic flux (Φ/Φ )
Ruthenate superconductor: Sr 2 RuO 4 (Y. Maeno, 1994) perovskite structure but Cu-free (T c = 1.5 K) multiple superconducting bands close to a ferromagnetic transition electrodynamics non-local (ξ ~ λ) unusual Ru interface 3K phase suspected to be unconventional suspected to be p-wave suspected to break time-reversal symmetry Proposed order parameter: complex p x ip y state (M. Rice and M. Sigrist) 2D analogue of 3 He A-phase k y Isotropic energy gap (magnitude) π/2 k x 3π/2 Continuous linear phase variation Broken time-reversal symmetry π p x ip y π p x -ip y Possibility of chiral domains 3π/2 π/2
Critical current modulation in Sr 2 RuO 4 /Au/Pb junctions Current (ma) 1-1 -2-1 1 2 Voltage (µv) Critical current Applied magnetic field Many features never seen in cuprates or conventional superconductors: Polarity asymmetry Hysteresis Abrupt jumps in critical current Two-level telegraph switching noise Different patterns on different crystals/faces/thermal cycles
Hysteresis in magnetic field sweeps Voltage(µV) 15 1 5 Retraces below threshold field (~1.2G for this sample) Constant hysteresis above threshold field Hysteresis heals if sweep reduced (de-gaussing?) -5 Pinned domains interacting with magnetic field? -15-1 -5 5 1 15 Applied field (mg)
Critical current switches noise in SRO junctions 6 Abrupt switches -256 Telegraph noise Critical current (ma) 5 4 3 2 1-1. -.5..5 1. Applied field (G) Voltage (µv) Critical current (ma) 5-3 4 3-35 2-41 -1. -1. -.5 -.5...5.5 1. 1. Applied field field (G)(mG) Switching noise in timetraces -1-5 start Voltage(µV) -1-15 end Voltage (µv) -11-12 -2-3 -2-1 1 2 3 Applied flux (mg) after field sweep -13 1 2 3 Time (s)
Chiral order parameter domains Chiral domains explain interference patterns, hysteresis, and switching noise Domain size ~ 1µm (deduced from number of oscillations in diffraction patterns) Chiral currents flow around domain edges --- not yet observed Motion of a single domain wall dramatically changes the critical current diffraction pattern accounts for switching noise observed Configuration A I c /I c.6.3 A B Configuration B. -1-5 5 1 Magnetic flux (Φ/Φ )
Diffraction patterns: chiral domains δ = Critical current (I/I ) 1..8.6.4.2. -1-5 5 1 Magnetic flux (Φ/Φ ) δ = π Simulation (1 domains) Critical current (I/I ).5.4.3.2.1. -15-1 -5 5 1 15 Magnetic flux (Φ/Φ ) Critical current (ma) 5 4 3 2 1-1. -.5..5 1. Applied field (G) Measurement Critical current (µa) 5 4 3 2 1-1 -5 5 1 Applied field (mg)
Critical current enhancement by magnetic field cooling Chiral domain currents couple to applied magnetic fields Applied field breaks chiral degeneracy, favoring one chirality Critical current (µa) 1 8 6 4 2 Zero-field cooled Critical current (µa) 1 8 6 4 2 Fieldcooled ~ 1mG -8-6 -4-2 2 4 6 8 Applied field (mg) -8-6 -4-2 2 4 6 8 Applied field (mg)
Junction scaling to verify the chiral domain size Goal: make range of junction sizes to determine domain size Approach: pattern wide single junction with Focused Ion Beam etching (5µm) 2 to (.5µm) 2 1µm 1µm
Onset of chiral domains in larger junctions - verifies 1µm scale Critical Current (µa) 35 3 25 2 15 1 5.5µm x.5µm 1µm x 1µm -4-2 2 4-4 -2 2 4 Applied Field (G) Applied Field (G) Cricital Current (µa) 6 5 4 3 2 1 2µm x 2µm 4µm x 4µm 24 22 15 Critical Current (µa) 2 18 16 14 12 1 Critical Current (µa) 1 5 8-6 -4-2 2 4 6 Applied Field (G) -2-1 1 2 Applied Field (G)
Heavy Fermion superconductor: UPt 3 Proposed order parameter symmetry --- two distinct superconducting phases temperature-induced real to complex transition in cooling (k x ik y ) 2 k z (k x2 -k y2 ) k z
Temperature evolution of the order parameter Δ R Δ Δ I T T c- T c Imaginary component turns on at T c- and lifts nodes Δ ~ (k x ik y ) 2 at low temperatures
Crystals by Bill Halperin (Northwestern) in floating zone furnace (RRR~1) Surfaces polished to.3 microns Barrier Cu/Counterelectrode Pb Measured with SQUID potentiometer Sample Fabrication/Measurement 1 2.75 2.5 Current (µa) 5-5 I (ma) 2.25 2. 1.75 1.5 44 KHz 33 KHz 22 KHz 11 KHz -1 1.25 -.3 -.2 -.1..1.2.3 Voltage (nv) 1. 1 2 3 4 5 6 7 8 9 V (h*f/2*e) f=11khz
Critical current vs. Temperature 1 1 T C - 8 Critcal current (µa) 8 6 4 2 I C (µa) 6 4 2 T C 48 5 52 54 56 58 T (mk) 1 2 3 4 5 6 Temperature (mk) Observe both upper and lower temperature superconducting phases opportunity to study symmetry transition
Low T Josephson Interferometry: B-phase Single-face measurements Corner junction measurements 25 cooled from room temp I C (µa) 15 1 35mK 315mK 325mK 345mK I C (µa) 2 15 1 6mK 7mK 8mK 9mK 1mK 11mK 12mK 14mK 5 5-4 -3-2 -1 1 2 3 4 Magnetic field (mg) -5-25 25 5 Applied field (mg) Fraunhofer-like patterns Patterns retrace no hysteresis, no switching noise no flux trapping Asymmetric patterns --- consistent with phase shifts other than or π Patterns change on successive cooling --- consistent with broken chiral symmetry or chiral domains
Data Simulation Low temperature B-phase All data is consistent with a complex order parameter of I C (µa) 3 25 2 15 1 T=7mK 7% the E2u form: 5-5 -25 25 5 Field (mg) (k x ik y ) 2 k z 2 T=6mK 15 2% I C (µa) 1 5 25-5 -25 25 5 T=6mK Field (mg) 2 15 1% I C (µa) 1 5-2 -15-1 -5 5 1 15 2 Field (mg)
Directional tunneling: distinguishing the two SC phases Tunneling into different directions on a crystal with as-grown surfaces Directions spaced at 45º 5 45º 4 T C - T C Critical current onsets are consistent with E 2u state I C (µa) 3 2 Tunneling into lobe Tunneling into node 1 47 48 49 5 51 52 53 54 55 T (mk) Evidence for gapping of nodes in the transition to the chiral (low T c ) phase
Exploring the Angular Dependence 1 cm measurement calculation
Exploring the Angular Dependence --- onset of supercurrent 1 8 54 Ic (µa) 6 4 2 Onset of I c (mk) 52 5 48 49 5 51 52 53 54 T (mk) 1 2 3 4 5 6 7 8 9 Angle from a-axis (degrees) nodes lobes Onset of second component (complex order parameter) Onset of primary component (real order parameter)
Why is the p x ip y symmetry exciting? 1. Exotic superconducting phase --- two component order parameter broken time-reversal symmetry 2. Complex chiral order parameter symmetry makes it a candidate for topologically-protected quantum computing d Half-Quantum Vortices carry Majorana fermions in core which exhibit non-abelian statistics --- allows topological phase operations Rotate d-vector into plane nucleates half-quantum vortices Protects against detrimental decoherence effects that plague conventional quantum computing schemes Analogous to the 5/2-quantum Hall state