Superconductivity Electrical resistance r pure metal a is

Superconductivity Electrical resistance r pure metal a is a material constant metal with impurities 0. 1 K (isotopic shift of the critical temperature) 1

Superconductivity Heike Kamerlingh Onnes 1913 Nobel prize in physics The superconductivity was discovered in 1911 by Heike Kamerlingh Onnes at the Leiden University. At 4. 2 K (-296°C), he observed a disappearance of resistivity in mercury. His experiments were made possible by the condensation of helium (1908). 2

Superconductivity Superconducting elements Al Cd Ga Hg In Ir La Mo Nb Os Pb Re T [K] 1. 19 0. 56 1. 09 4. 00 3. 40 0. 14 5. 00 0. 92 9. 13 0. 65 7. 19 1. 70 Ru Sn Ta Tc Th Ti Tl U V Zn Zr T [K] 0. 49 3. 72 4. 48 8. 22 1. 37 0. 39 2. 39 0. 68 5. 30 0. 87 0. 55 3

Isotopic Shift Material T [K] a Zn Cd Sn Hg Pb Tl Ru Os Mo Nb 3 Sn Mo 3 Ir Zr 0. 87 0. 56 3. 72 4. 00 7. 19 2. 39 0. 45± 0. 05 0. 32± 0. 07 0. 47± 0. 02 0. 50± 0. 03 0. 49± 0. 02 0. 61± 0. 10 0. 49 0. 65 0. 92 18 0. 00± 0. 05 0. 15± 0. 05 0. 33 0. 08± 0. 02 0. 33± 0. 03 0. 55 0. 00± 0. 05 4

Superconductivity Temperature dependence of the critical magnetic field Superconductor in a magnetic field Hc normal state Superconductor: Meissner effect superconducting state Tc T Otherwise: -10 -6 5

Meissner-Ochsenfeld effect 6

Magnetic levitation train 7

Superconductor in a magnetic field External field: Inner field: Magnetization: Work per unit of volume (magnetization direction of a superconductor is opposite to the magnetic field direction) Energy of a superconductor within a magnetic field is higher than without a magnetic field This is caused by the “superconducting” electrons 8

Transition between normal and superconducting state Thermodynamic consideration 9

Superconductivity S. L. Bud’ko and P. C. Canfield: Temperature-dependent Hc 2 anisotropy in Mg. B 2 as inferred from measurements on polycrystals, Phys. Rev. B 65 (2002) 212501. 10

Crystal structures of La 2 -x. Bax. Cu. O 4 and YBa 2 Cu 3 O 7 -x La 2 -x. Bax. Cu. O 4 Space group: Bmab Lattice parameters: a = 5. 33915(9) Å b = 5. 35882(9) Å c = 13. 2414(2) Å YBa 2 Cu 3 O 7 -x Space group: Pmmm Lattice parameters: a = 3. 856(2) Å b = 3. 870(2) Å c = 11. 666(3) Å a b a/ 2 < c/3 < a a b c/3 11

Superconductivity superconducting normal state 12

Theories of Superconductivity Superelectrons : • No scattering • Entropy of the system is zero (the system is perfectly ordered) • Large coherence length 13

London Theory (Meissner Effect) Ohm: London: (static conditions) Maxwell: =0 Solution: Meissner effect: B x 14

Consequences of the London Theory 15

Coherence Length The distance in which the width of the energy gap, in a spatial variable magnetic field, doesn’t change essentially. London: 16

BCS Theory of Superconductivity J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 106 (1957) 162. J. Bardeen, L. N. Cooper and J. R. Schrieffer, Phys. Rev. 108 (1957) 1175. 1. Interactions between electrons can cause a ground state, which is separated from the electronically excited states by an energy gap. However: there also superconductors without an energy gap! 17

BCS Theory of Superconductivity 2. The energy gap is caused by the interaction between electrons via lattice vibrations (phonons). One electron distort the crystal lattice, another electron “sees” this and assimilate his energy to this state in a way, which reduces the own energy. That’s how the interaction between electrons via lattice vibrations work. 18

BCS Theory of Superconductivity 3. The BCS theory delivers the London penetration depth for the magnetic field and the coherence length. Thereby the Meissner effect is explained. London: Meissner: Coherence length: 19