Superconductors: Basic Concepts

1. Superconductors: Basic Concepts • Daniel Shantsev • AMCS group • Department of Physics • University of Oslo • History • Superconducting materials • Properties • Understanding • Applications Research School Seminar February 6, 2006

2. Discovered by Kamerlingh Onnes in 1911 during first low temperature measurements to liquefy helium Whilst measuring the resistivity of “pure” Hg he noticed that the electrical resistance dropped to zero at 4.2K How small is zero? A lead ring carrying a current of several hundred ampères was kept cooled for a period of 2.5 years with no measurable change in the current 1913 Discovery of Superconductivity

3. Fe (iron) Tc=1K (at 20GPa) Nb (Niobium) Tc=9K Hc=0.2T Transition temperatures (K) and critical fields are generally low Metals with the highest conductivities are not superconductors The magnetic 3d elements are not superconducting ...or so we thought until 2001 The superconducting elements Transition temperatures (K) Critical magnetic fields at absolute zero (mT)

4. HgBa2Ca2Cu3O9 (under pressure) 160 Highest Tc 138 K (at normal pressure) 140 HgBa2Ca2Cu3O9 TlBaCaCuO 120 BiCaSrCuO 100 YBa2Cu3O7 Superconducting transition temperature (K) Liquid Nitrogen temperature (77K) 80 60 MgB2 40 (LaBa)CuO 1987 Nb3Ge Nb3Sn NbN 20 NbC Nb Pb Hg V3Si 1910 1930 1950 1970 1990 Superconductivity in alloys and oxides

5. Magnetic field is excluded from • a superconductor • (Meissner & Ochsenfeld, 1933) Ideal diamagnet General properties • Zero resistance at T<Tc • (Kamerlingh Onnes, 1911) Ideal conductor (the resistive state is restored in a magnetic field or at high transport currents)

6. 2 Superconductivity – Quantum phenomenon at macroscale Quantization of magnetic flux Deaver & Fairbank, 1961 + B Long hollow cylinder the magnetic flux through a superconducting ring is an integer multiple of a flux quantum

7. Experimental evidence for BCS Bardeen Cooper Schriffer 1972 BCS Theory (1) Electrons combine in Cooper pairs due to interactions with phonons x (2) All Cooper pairs (bosons) condense into one quantum state separated by an energy gap from excited states Metal: many individual electrons Superconductor: all electrons move coherently

8. Ivar Giaver (UiO) 1973 direct experimental evidence of the existence of the energy gap N S From the Nobel lecture, http://nobelprize.org/physics/laureates/1973/

9. 2 BCS: All Cooper pairs are desribed by one wave function:  =|| ei Superconductivity – Quantum phenomenon at macroscale Quantization of magnetic flux Deaver & Fairbank, 1961 + B  dx = 2 /0 = 2k

10. I S S V I = Ic sin (1 - 2) Supercurrent Phase of the wave function Josephson interferometer Most sensitive magnetometer – SQUID (superconducting quantum interference device) SQUID sensitivity 10-14 T Heart fields 10-10 T Brains fields 10-13 T B. Josephson 1973 Josephson effect What is the resistance of the junction? For small currents, the junction is a superconductor!

11. Magnetic field Hc Normal state Type I Meissner state • Vortex lattice • A. Abrikosov • (published 1957) Temperature Tc Hc2 Normal state Mixed state (vortex matter) Type II 2003 Hc1 Meissner state Temperature Tc

12. Coherence length x London penetration depth l  x < l type II NS interface  x > l type I NS interface Vortex normal core x J B(r) l B dA = h/2e = 0 Flux quantum: superconductor 

13. V. L. Ginzburg, L. D. Landau 2003 Ginzburg-Landau functional: Ginzburg-Landau Theory Order parameter? a T-Tc

14. High-current Cables ~100 times better than Cu In May of 2001 some 150,000 residents of Copenhagen began receiving their electricity through high-Tc superconducting material (30 meters long cable).

15. Magnetic Resonance Imaging (MRI) Magnetoencephalography • 75 million MRI scans per year • Higher magnetic field means higher sensitivity Measuring tiny magnetic fields in the human brain • Electric generators made with superconducting wire • Superconducting MagneticEnergy Storage System • Superconductor-based transformers and fault limiters • Infrared sensors • Magnetic shielding devices • Ultra-high-performance filters • etc

16. Most high energy accelerators now use superconducting magnets. The proton accelerator at Fermilab uses 774 superconducting magnets (7 meter long tubular magnets which generate a field of 4.5 Tesla) in a ring of circumference 6.2 km. The coils are made of NbSn3 or NbTi embedded in form of fine filaments (20 mm diameter) in a copper matrix Image from BNL

17. Superconducting magnet designed for the Alpha Magnetic Spectrometer at the International Space Station to help look for dark matter, missing matter & antimatter Image from U.Geneva

18. Levitation: MagLev Trains Miyazaki Maglev Test Track, 40 km • No friction • Super-high speed • Safety • Noiseless 581 km/h

19. Ba J Lorentz force: f = JB Jc f Vortex pinning Record trapped field: 17 Tesla Field distribution presintered 123-pellet • The maximal field in the magnets, • The maximal current in the cables • are determined by vortex pinning • => it’s important to study vortices Top-seeded melt-growth

20. Magneto-optical imaging Åge Olsen: Observation of what Vortices do NbSe2field-cooled to 4.3 K Sanyalak Niratisairak: Characterization of MO-films 10 m Jørn Inge Vestgården: Calculation of Vortex distributions Superconductivity Lab @ UiO