Superconductivity, Exercises of Advanced Physics

Download Superconductivity and more Exercises Advanced Physics in PDF only on Docsity! 1 Heike Kamerlingh Onnes’s Discovery of Superconductivity The turn-of-the-century race to reach temperatures approaching absolute zero led to the unexpected discovery of electric currents that flowed with no resistance 2 Temperature R e si st iv it y Kelvin (1902) Matthiessen (1864) Dewar (1904) Electrical resistivity at low temperatures Kelvin: Electrons will be frozen – resistivity grows till . Dewar: the lattice will be frozen – the electrons will not be scattered. Resistivity wiil decrese till 0. Matthiesen: Residual resistivity because of contamination and lattice defects. Hydrogen was liquefied (boiling point 20.28 K) for the first time by James Dewar in 1898 One of the scientific challenge at the end of 19th and beginning of the 20th century: How to reach temperatures close to 0 K? 5 Superconductivity- discovery II •Liquid Helium (4K) (1908). Boiling point 4.22K. •Superconductivity in Hg TC=4.2K (1911) „Mercury has passed into a new state, which on account of its extraordinary electrical properties may be called the superconducting state“ H. Kamerlingh Onnes 1913 (Nobel preis 1913) Resistivity R=0 below TC; (R<10-23 cm, 1018 times smaller than for Cu) Superconducting Elements Superconducting Superconducting under high pressure or in thin films ae No|PulAmCm|Bk|Cf/EsFmiMdNolLr | 7 Further discoveries 1986 (January): High Temperature Superconductivity (LaBa)2 CuO4 TC=35K K.A. Müller und G. Bednorz (IBM Rüschlikon) (Nobel preis 1987) 1987 (January): YBa2Cu3O7-x TC=93K 1987 (December): Bi-Sr-Ca-Cu-O TC=110K, 1988 (January): Tl-Ba-Ca-Cu-O TC=125K1993: Hg-Ba-Ca-Cu-O TC=133K (A. Schilling, H. Ott, ETH Zürich) 1911-1986: “Low temperature superconductors” Highest TC=23K for Nb3Ge Effect of Magnetic Field Critical magnetic field (HC) – Minimum magnetic field required to destroy the superconducting property at any temperature H0 – Critical field at 0K T - Temperature below TC TC - Transition Temperature Superconducting Normal T (K) TC H0 HC Element HC at 0K (mT) Nb 198 Pb 80.3 Sn 30.92 0 1C C T H H T             MEISSNER EFFECT • When the superconducting material is placed in a magnetic field under the condition when T≤TC and H ≤ HC, the flux lines are excluded from the material. • Material exhibits perfect diamagnetism or flux exclusion. • Deciding property • χ = I/H = -1 • Reversible (flux lines penetrate when T ↑ from TC) • Conditions for a material to be a superconductor i. Resistivity ρ = 0 ii. Magnetic Induction B = 0 when in an uniform magnetic field • Simultaneous existence of conditions Applications of Meissner Effect • Standard test – proof for a superconductor • Repulsion of external magnets - levitation Magnet Superconduct or Yamanashi MLX01 MagLev train 15 Classical model of superconductivity The lattice deformation creates a region of relative positive charge which can attract another electron. An electron on the way through the lattice interacts with lattice sites (cations). The electron produces phonon. 1957 John Bardeen, Leon Cooper, and John Robert Schrieffer During one phonon oscillation an electron can cover a distance of ~104Å. The second electron will be attracted without experiencing the repulsing electrostatic force . John Bardeen, Leon Neil Cooper, John Robert Schrieffer Nobel Prize in Physics 1972 "for their jointly developed theory of superconductivity, called the BCS-theory” e- e- Phonon Coherence length  Cooper pair model 17 Types of Superconductors Type I • Sudden loss of magnetisation • Exhibit Meissner Effect • One HC = 0.1 tesla • No mixed state • Soft superconductor • Eg.s – Pb, Sn, Hg Type II • Gradual loss of magnetisation • Does not exhibit complete Meissner Effect • Two HCs – HC1 & HC2 (≈30 tesla) • Mixed state present • Hard superconductor • Eg.s – Nb-Sn, Nb-Ti - M HH C Superconducting Normal Superconducting -M Normal Mixed HC1 HC HC2 H 21 Good electrical conductors are showing no superconductivity In case of good conductors is the interaction of carriers with the lattice very week. This is, however, important for superconductivity. BCS Theory: some consequences Isotope effect The Cooper-Pairs are created (“glued”) by the electron- phonon interaction. Energy of the phonons (lattice vibrations) depends on the mass of the lattice site . Superconductivity (Tc) should depend on the mass of the ions (atoms) creating the lattice. TC~M- For most of the low- temperature superconductors =0.5 22 What destroys superconductivity? High temperatures: strong thermal vibration of the lattice predominate over the electron-phonon coupling. Magnetic field: the spins of the C-P will be directed parallel. (should be antiparallel in C-P) A current: produces magnetic field which in turn destroys superconductivity. Current density Temperature Magnetic field 25 Penetration depth  depicts the distance where B(x) is e-time smaller than on the surface  0 (T)= 0 *(1-(T/T C )4)-0.5 T C E in dr in gt ie fe  TemperaturTemperature P en et ra tio n de pt h Superconductor 26 Ginzburg-Landau Parameter =/GL Tc  [nm] [nm]  Al 1.2 16 1600 0.01 Sn 3.7 34 230 0.16 Pb 7.2 37 83 0.4 <1/2=0.71 Superconductor Type I Tc  [nm] [nm]  Nb 9.3 39 38 1 Nb3Sn 18 80 3 27 YBa2Cu3O7 93 150 1.5 100 Rb3C60 30 247 2.0 124 Bi2Sr2Ca2Cu3O10 110 200 1.4 143 >0.71 Superconductor Type II 27 Superconductor type I (/GL<0.71) in a magnetic field Bi=Ba+0 M Superconducto r Bi=0 Normal conductor Bi=Ba Negative units ! The field inside the superconductor The field created on the surface of the superconductor compensating the outside fieldOutside field Outside field BaOutside field Ba In si d e fi e ld B i M a g n e ti za ti o n – μ 0 M