Introduction to superconductivity

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1 Introduction to superconductivity

2 Textbook: Introduction to superconductivity by A.C.Rose-Innes & E. H. Rhoderick 2 nd Ed. References: Introduction to superconductivity by M. Tinkham 2 nd Ed. superconductivity by C. P. Poole, Jr., H. A. Farach, and R. J. Creswick

3 Outline 1 Introduction-zero resistance 2. Perfect diamagnetism 3. Electrodynamics/The London theory 4. The critical magnetic field 5. Thermodynamics of the transition 6. The intermediate state 7. Transport currents in superconductors 8. The superconducting properties of small specimens 9. Ginzburg- Landau theory 9. The microscopic theory/bcs theory 10. Tunneling/Josephson effect 11. Type-II superconductivity 12. Hi-Tc superconductors

Transport currents in superconductors 8. The superconducting properties of small specimens 9.

4 1. Introduction- Zero resistance

5 Zero resistance resistivity impure metal resistivity superconductor Perfectly pure metal T T C T Residual resistivity ρ 0 Critical temperature transition temperature

6 Discovery of superconductivity H. Kamerlingh Onnes (Leiden University) He was the first to liquify helium (1908), for which he was awarded the Nobel prize in 1913, and he discovered superconductivity in 1911 According to Onnes, "Mercury has passed into a new state, which on account of its extraordinary electrical properties may be called the superconductive state". H. K. Onnes, Commun. Phys. Lab.12,120, (1911)

awarded the Nobel prize in 1913, and he discovered superconductivity in 1911 According to Onnes,

7 100 years in superconductivity Discovery of superconductivity H. Kamerlingh Onnes(1911) in Hg 1913 Nobel prize Perfect diamagnetism: Meissner and Ochsenfeld(1933) London equation: F. and H. London(1933) Ginzburg-Landau theory: 1950s 2003 Nobel prize (with Abrikosov) Isotope effect: H. Frohlich(1950) BCS theory: J. Bardeen, L. Cooper and J.R. Schrieffer(1957) 1972 Nobel prize Tunneling: Josephson (1957) 1973 Nobel prize Hi-Tc superconductivity: J. G. Bednorz and K. A. Muller(1986) in Ba-La-Cu-O system Nobel prize

London(1933) Ginzburg-Landau theory: 1950s 2003 Nobel prize (with Abrikosov) Isotope effect: H. Frohlich(1950) BCS theory: J.

8 Known superconductive elements

9 Transition temperatures Nb Tc Lead (Pb) V Lanthanum (La) Tantalum(Ta) Mercury (Hg) Tin (Sn) Indium (In) Thallium (Tl) Rhenium (Re) Protactinium (Pa) Thorium (Th) Aluminum (Al) Gallium (Ga) Molybdenum (Mo) Zinc (Zn) Osmium (Os) Zirconium (Zr) 9.25K 7.80 K K 5.40 K 4.88 K 4.47 K 4.15 K 3.72 K 3.41 K 2.38 K K 1.40 K 1.38 K K K K 0.85 K 0.66 K 0.61 K BCC(Type 2) HEX(Type 2) FCC BCC(Type 2) HEX BCC RHL TET TET HEX HEX TET FCC FCC ORC BCC HEX HEX HEX Americium (Am) Cadmium (Cd) Ruthenium (Ru) Titanium (Ti) Uranium (U) Hafnium (Hf) Iridium (Ir) Beryllium (Be) Tungsten (W) Platinum (Pt)* Rhodium (Rh) MgB 2 39K Nb 3 Ge 23.2K 0.60 K K 0.49 K 0.40 K 0.20 K K K K K K K *compacted powder HEX HEX HEX HEX ORC HEX FCC HEX BCC FCC FCC

61 K BCC(Type 2) HEX(Type 2) FCC BCC(Type 2) HEX BCC RHL TET TET HEX HEX TET FCC FCC ORC BCC HEX HEX HEX Americium (Am) Cadmium (Cd) Ruthenium (Ru) Titanium (Ti) Uranium (U) Hafnium (Hf) Iridium (Ir)

10 Transition temperature(hi-tc) Bednorz and Muller, Z. Physik B64, 189, (1986) M. K. Wu, et al., Phys. Rev. Lett. 58, 908 (1987)

13 Persistent current The inductance of the loop 8r L= µ 0r ln 2 a The resistance of the loop 2rρ R = 2 a 2a r The time constant τ = L R () = (0) t it i e τ ρ < Ω m For Cu ρ ~ 1.56 µω cm

14 Resistanceless circuit The flux due to external field threading a closed loop Φ x =AB app Φ x The induction law yields: db = + dt a A Ri L db dt a A = di L dt di dt For a resistanceless loop: Li + AB a = constant The total magnetic flux threading a closed loop Φ= Φ x +Φ L =constant Φ x =AB app i Φ L =Li B app

dt di dt For a resistanceless loop: Li + AB a = constant The total magnetic

15 Superconducting solenoid The current is generated by the power supply P, and is adjusted by the rheostat R. Once the current is brought to the desired value, the switch XY can be closed. Since S and XY form a closed resistanceless loop, the magnetic field flux threaded by the loop remains the same. Now one can disconnect the power supply and the solenoid runs in the persistent mode.

Since S and XY form a closed resistanceless loop, the magnetic field flux threaded by the loop

16 2. Perfect diamagnetism

17 Perfect diamagnetism superconductor Perfect diamagnetism Perfect conductor Constant magnetic flux Flux exclusion: zero field cooled Flux expulsion: field cooled B = 0 Meissner effect B = 0 Recall the result deduced in page 14

zero field cooled Flux expulsion: field cooled B = 0

18 superconductor Perfect conductor ZFC FC

19 Permeability ( ) ( ) B= µ H + M = µ + χ H M = H χ = 1 Magnetic susceptibility Magnetic permeability µ = 0

20 + Bapp = µ H M = H 0 (inside the sphere) A dipole field outside the sphere B

21 Surface currents B =µ J 0 J = M

22 Hole in Superconductor

23 Surface currents

24 Penetration depth Boundary condition H = H H app H in H app = H in B app B in For perfect diamagnetism B app = µ 0Happ B in = 0 λ For a finite current density, the surface current is distributed within a depth, λ

25 London theory Bx ( ) = B(0) e x / λ B app superconductor B(x) λ x

26 Variation with temperature λ λ = ( 1 t ) 1/2 t = T T C superconductor The measurement of penetration depth Self inductance of the solenoid, L is a function of penetration depth The tank circuit form an oscillator of a typical frequency L + C _ Tank circuit

SUPERCONDUCTIVITY. PH 318- Introduction to superconductors 1

SUPERCONDUCTIVITY. PH 318- Introduction to superconductors 1 SUPERCONDUCTIVITY property of complete disappearance of electrical resistance in solids when they are cooled below a characteristic temperature. This temperature is called transition temperature or critical