Superconductivity Alexey Ustinov Universität Karlsruhe WS 2008-2009 Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 1
Lectures October 20 Phenomenon of superconductivity October 27 Magnetic properties and thermodynamics November 3 Electrodynamics and magnetic flux quantization November 10 Ginzburg-Landau theory November 17 Type I and II superconductors and vortices November 24 Basic ideas of BCS theory December 1 Energy gap and tunneling December 8 Josephson effect December 15 SQUIDs December 22 Long junction and solitons January 12 SNS structures and Andreev reflection January 19 Superconducting electronics January 26 Detectors, mixers, oscillators February 2 Superconducting qubits Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 2
Literature 1. V.V. Schmidt "The physics of superconductors", Eds. P.Müller and A.V.Ustinov, Springer, 1997. 2. M. Tinkham "Introduction to superconductivity", McGraw-Hill, 2nd ed., 1996. 3. W. Buckel and R. Kleiner, "Superconductivity: Fundamentals and Applications", Wiley-VCH, 2004 Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 3
Phenomenon of superconductivity Introduction Historic milestones Superconducting materials Meissner effect Levitation experiments Magnetic flux quantization Josephson effect Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 4
Historic milestones 1908 Making liquid helium (4.2 K) 1911 Discovery of zero resistance 1933 Meissner effect 1935 Londons theory 1950 Ginzburg-Landau theory 1957 Bardeen-Cooper-Schrieffer (BCS) theory 1960 Magnetic flux quantization 1962 Josephson effect 1986 High-temperature superconductors Nobel Prizes Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 5
methyl chloride ethylene oxygen air hydrogen The cycles for the various gases are joined in cascades, so that the cold bath, which can be maintained by a previous cycle, also serves to liquefy at a lower temperature the gas which circulates in the following cycle. Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 6
The compressed helium comes, after suitable precooling, into the refrigerator, where hydrogen is evaporating at the air pump, runs through the regenerator spiral and expands at the throttle valve. The liquid formed according to the Linde process gathers in the lower portion of the vacuum glass vessel. In order to be able to observe the liquid helium this portion is transparent and is surrounded by a vacuum glass vessel which is kept filled with liquid hydrogen, which is again protected by a transparent vacuum glass vessel containing liquid air. Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 7
Introduction Superconductivity was discovered by Kamerlingh-Onnes in 1911 in mercury (Hg), having T c 4 K.. Mercury has passed into a new state, which on account of its extraordinary electrical properties may be called the superconductive state Dependence of the resistance on temperature Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 8
Superconducting materials Cold liquids required for reaching low temperatures: helium 4 He (4.2 K) hydrogen H 2 (20 K) neon Ne (27 K) nitrogen N 2 (77 K) pure metals alloys modern 100 liter liquid helium dewar Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 9
Superconducting elements Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 10
ceramic materials * under pressure Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 11
Superconducting materials Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 12
Introduction Superconductivity is destroyed: by increasing temperature at T > T c by large magnetic field H > H c Phase diagram of a superconductor in the H T plane is described by an empirically found formula: H T diagram for the superconducting state Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 13
Meissner effect Discovered by Walther Meissner and Robert Ochsenfeld in 1933. Example 1: a conductor Magnetic field induces a screening current (Lentz rule) which generates the opposite field. In an ideal conductor: A real conductor in magnetic field. According to Maxwell s equation inside the conductor we have Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 14
Meissner effect Example 2: an ideal conductor Magnetic field induces a screening current (Lentz rule) which generates an opposite magnetic field inside the sample An ideal conductor in magnetic field Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 15
Meissner effect Example 3: finally, a superconductor superconductor magnetic field ON Meissner effect: Superconductor always expels the magnetic flux magnetic field ON + relaxation conductor A superconductor in magnetic field Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 16
Levitation experiments Levitation of a magnet: magnet superconductor Bruce Gowe Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 17
Magnetic flux quantization area S take a ring at T>T c apply external magnetic field H cool down to T<T c and switch off the external field Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 18
Magnetic flux quantization Φ = A d H S Experimental result: how large is the magnetic flux in the ring? Φ = n Φ 0 where 15 Φ0 = 2.07 10 V s n = 0, ± 1, ± 2,... S. Deaver and W.M. Fairbank, Phys. Rev. Lett. 7, 43 (1961) R. Doll and M. Näbauer, Phys. Rev. Lett. 7, 51 (1961) Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 19
Josephson effect superconductor tunnel barrier superconductor current I Ψ Ψ exp ( i 1) 1 = Ψ1 θ = Ψ exp ( i 2) 2 2 θ Ψ1 = Ψ 2 superconducting phase difference: ϕ = θ 1 θ 2 Josephson relations I s = I c sin ϕ V = dϕ 2e dt Electromagnetic radiation at the frequency f f = V Φ 0 Alexey Ustinov WS2008/2009 Superconductivity: Lecture 1 20