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

Discovery of Superconductivity Whilst measuring the resistivity of “pure” Hg he noticed that the electrical resistance dropped to zero at 4.2K Discovered by Kamerlingh Onnes in 1911 during first low temperature measurements to liquefy helium 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

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

Superconducting transition temperature (K) Superconductivity in alloys and oxides Hg Pb Nb NbC NbN V 3 Si Nb 3 Sn Nb 3 Ge (LaBa)CuO YBa 2 Cu 3 O 7 BiCaSrCuO TlBaCaCuO HgBa 2 Ca 2 Cu 3 O 9 (under pressure) HgBa 2 Ca 2 Cu 3 O 9 (under pressure) Liquid Nitrogen temperature (77K) 1987 Highest T c 138 K (at normal pressure) MgB 2

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

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

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

Ivar Giaver (UiO) 1973 direct experimental evidence of the existence of the energy gap From the Nobel lecture, NS

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

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

T c Temperature T c Mixed state (vortex matter) Meissner state Normal state H c1 H c2 Type II T c Temperature T c Normal state Meissner state HcHcHcHc Magnetic field Type I Vortex lattice A.A. Abrikosov (published 1957) 2003

12 Vortex  B dA = h/2e =  0 Flux quantum:  J B(r) normal core superconductor Coherence length  London penetration depth  type II  type I NS interface NS interface 

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

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).

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

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 NbSn 3 or NbTi embedded in form of fine filaments (20  m diameter) in a copper matrix Image from BNL

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

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

presintered 123-pellet Top-seeded melt-growth JcJc Field distribution Vortex pinning Record trapped field: 17 Tesla The maximal field in the magnets, The maximal current in the cables are determined by vortex pinning => it’s important to study vortices

Magneto-optical imaging NbSe 2 field-cooled to 4.3 K 10  m Sanyalak Niratisairak: Characterization of MO-films Åge Olsen: Observation of what Vortices do Jørn Inge Vestgården: Calculation of Vortex distributions Superconductivity UiO