Superconductivity and Superfluidity

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1 Superconductivity and Superfluidity Contemporary physics, Spring 2015 Partially from: Kazimierz Conder Laboratory for Developments and Methods, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland

2 Resistivity Electrical resistivity at low temperatures Kelvin (1902) Matthiessen (1864) 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. Temperature Dewar (1904) Matthiesen: Residual resistivity because of contamination and lattice defects. One of the scientific challenge at the end of 19 th and beginning of the 20 th century: How to reach temperatures close to 0 K? Hydrogen was liquefied (boiling point K) for the first time by James Dewar in

Superconductivity- discovery I 1895 William Ramsay in England discovered helium on the earth 1908 H. Kamerlingh Onnes liquefied helium (boiling point 4.

3 Superconductivity- discovery I 1895 William Ramsay in England discovered helium on the earth 1908 H. Kamerlingh Onnes liquefied helium (boiling point 4.22 K) Resistivity at low temperatures- pure mercury (could repeatedly distilled producing very pure samples). Repeated resistivity measurements indicated zero resistance at the liquid-helium temperatures. Short circuit was assumed! During one repetitive experimental run, a young technician fall asleep. The helium pressure (kept below atmospheric one) slowly rose and, therefore, the boiling temperature. As it passed above 4.2 K, suddenly resistance appeared. Hg T C =4.2K From: Rudolf de Bruyn Ouboter, Heike Kamerlingh Onnes s Discovery of Superconductivity, Scientific American March 1997

2K (1911) Mercury has passed into a new state, which on account of its extraordinary

4 Superconductivity- discovery II Liquid Helium (4K) (1908). Boiling point 4.22K. Superconductivity in Hg T C =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 T C ; (R<10-23 cm, times smaller than for Cu) 4

Further discoveries 1911-1986: Low temperature superconductors Highest T C =23K for Nb 3 Ge 1986 (January): High Temperature Superconductivity (LaBa) 2 CuO 4 T C =35K K.A. Müller und G.

5 Further discoveries : Low temperature superconductors Highest T C =23K for Nb 3 Ge 1986 (January): High Temperature Superconductivity (LaBa) 2 CuO 4 T C =35K K.A. Müller und G. Bednorz (IBM Rüschlikon) (Nobel preis 1987) 1987 (January): YBa 2 Cu 3 O 7-x T C =93K 1987 (December): Bi-Sr-Ca-Cu-O T C =110K, 1988 (January): Tl-Ba-Ca-Cu-O T C =125K 1993: Hg-Ba-Ca-Cu-O T C =133K (A. Schilling, H. Ott, ETH Zürich) 5

6 140 HgBa 2 Ca 2 Cu 3 O Tl 2 Sr 2 Ca 2 Cu 3 O 10 T C [K] Liquid nitrogen Bi 2 Sr 2 Ca 2 Cu 3 O 10 YBa 2 Cu 3 O Hg Pb Nb NbN La 2-x Sr x CuO 4 MgB 2 Nb 3 Ge Nb Cs 2 RbC 60 3 Sn Ba 1-x K x BiO 3 Na x WO 3 BaPb 1-x Bi x O 3 L NbO He Year 6

7 DC Resistance Magnetic Induction I The Three Hallmarks of Superconductivity Zero Resistance Complete Diamagnetism Macroscopic Quantum Effects Flux F V T>T c T<T c 0 T c Temperature 0 T c Temperature Flux quantization F = nf 0 Josephson Effects

Zero resistivity Low temperatures: LN 2-196 0

8 Zero resistivity Low temperatures: LN C (77K) The current can flow years!! 8

Ochsenfeld (1933) On the surface of a superconductor (T<T C ) superconducting current will

9 Meissner-Ochsenfeld-effect A superconductor is a perfect diamagnet. Superconducting material expels magnetic flux from the interior. W. Meissner, R. Ochsenfeld (1933) On the surface of a superconductor (T<T C ) superconducting current will be induced. This creates a magnetic field compensating the outside one. Screening (shielding ) currents Magnetic levitation 9

10 Meissner-Ochsenfeld-effect Levitation train 10

11 How does it work? 11

12 Classical model of superconductivity 1957 John Bardeen, Leon Cooper, and John Robert Schrieffer An electron on the way through the lattice interacts with lattice sites (cations). The electron produces phonon. During one phonon oscillation an electron can cover a distance of ~10 4 Å. The second electron will be attracted without experiencing the repulsing electrostatic force. The lattice deformation creates a region of relative positive charge which can attract another electron. 12

13 John Bardeen, Leon Neil Cooper, John Robert Schrieffer Nobel Prize in Physics 1972 "for their jointly developed theory of superconductivity, called the BCS-theory Cooper pair model e - Phonon Coherence length e - Isotope effect: T C ~M -

.) Pauli-Principle every energy level can be occupied with maximum two electrons with opposite spins.

14 Fermie and Bose-Statistic Energy Energy Density of states Density of states Fermions- elemental particles with 1/2 spin (e.g. electrons, protons, neutrons..) Pauli-Principle every energy level can be occupied with maximum two electrons with opposite spins. Cooper-Pairs are created with electrons with opposite spins. Total spin of C-P is zero. C-P are bosons. Pauli-Principle doesn t obey. All C-P can have the same quantum state with the same energy. It is a collective mode. 14

15 What destroys superconductivity? A current: produces magnetic field which in turn destroys superconductivity. Current density Magnetic field Magnetic field: the spins of the C-P will be directed parallel. (should be antiparallel in C-P) Temperature High temperatures: strong thermal vibration of the lattice predominate over the electron-phonon coupling. 15

16 Coherence length (Xi) Superconductor Concentration C-P SC SL I x< GL SC SL Coherence length is the largest insulating distance which can be tunneled by Cooper-Pairs. GL Coherence length is the distance between the carriers creating a Cooper-Pair. 16

Nobel Prize in Physics 1973 Brian David Josephson "for his theoretical predictions of the properties of a supercurrent through a tunnel barrier, in particular those phenomena which are generally

17 Nobel Prize in Physics 1973 Brian David Josephson "for his theoretical predictions of the properties of a supercurrent through a tunnel barrier, in particular those phenomena which are generally known as the Josephson effects". Josephson discovered in 1963 tunnelling effect being 23-years old PhD student The superconducting tunnel Josephson) junction (superconductor insulator superconductor tunnel junction (SIS) is an electronic device consisting of two superconductors separated by a very thin layer of insulating material SC SL I SC SL x< GL

18 Penetration depth Eindringtiefe Penetration depth Superconductor (T)= 0 *(1-(T/T C ) 4 ) -0.5 depicts the distance where B(x) is e-time smaller than on the surface 0 Temperature T C 18

16 Pb 7.2 37 83 0.4 >0.71 Superconductor Type II T c [nm] [nm] Nb 9.

19 Ginzburg-Landau Parameter = / GL <1/ 2=0.71 Superconductor Type I T c [nm] [nm] Al Sn Pb >0.71 Superconductor Type II T c [nm] [nm] Nb Nb 3 Sn YBa 2 Cu 3 O Rb 3 C Bi 2 Sr 2 Ca 2 Cu 3 O

compensating the outside field Negative units!

20 Superconductor type I ( / GL <0.71) in a magnetic field Magnetization μ 0 M The field inside the superconductor B i =B a + 0 M Outside field The field created on the surface of the superconductor compensating the outside field Negative units! Inside field B i Outside field B a Outside field B a Superconductor B i =0 Normal conductor B i =B a 20

Magnetization μ 0 M Superconductor type II in a

Vortex-lattice in superconductor type II.

21 Magnetization μ 0 M Superconductor type II in a magnetic field B i =B a + 0 M Meissner phase Mixed phase Outside field B a Normal conductor Average inside field B i Outside field B a Vortex-lattice in superconductor type II. Magnetic flux of a vortex is quantized: F 0 =h/2e Tm 2 21

Temperature T STM (Scanning Tunneling Microscopy).

22 Magnetic induction B Superconductor type II. B-T-Diagram Normal state Mixed phase Meissner phase Temperature T STM (Scanning Tunneling Microscopy). Abrikosov-lattice in NbSe 2 H. Hess, R.B. Robinson, and J.V. Waszczak, Physica B 169 (1991)

23 Nobel Prize in Physics 2003 "for pioneering contributions to the theory of superconductors and superfluids". Alexei A. Abrikosov, Vitaly L. Ginzburg, Anthony J. Leggett

24 Superfluidity of Helium 24

25 Superconductivity and superfluidity Superconductivity superfluidity Dissipationless flow of electrons in a solid Light particles (electrons) Frictionless flow of a fluid Much heavier particles (atoms) A superconductor is a condensate of Cooper pairs, where the electrons comprising the Cooper pair are generally not right next to each other A superfluid is a condensate of atoms, and an atom is a local object Bose condensation of Cooper pairs (two electrons) Usually, Bose condensation of bosons (atoms), exception He3 25

26 High Temperature Superconductor. La 2-x Sr x CuO 4 (LaBa) 2 CuO 4 T C =35K K.A. Müller und G. Bednorz (IBM Rüschlikon 1986 ) Cu O La, Sr Temperature [K] 100 Antiferromagnet T N Insulator La 2-x Sr x CuO 4 Superconductor Metal Sr-content x, (holes per CuO 2 -layer) T C 2SrO 2Sr La + 2O x O + V O V O+ 0.5O 2 O x O+ 2h 26

27 Superconductivity Quantum Magnetism Strongly correlated electron systems Quantum Hall effect Disordered systems Heavy Fermions Topological phases 27

28 Discussion 28

Strongly Correlated Systems:

M.N.Kiselev Strongly Correlated Systems: High Temperature Superconductors Heavy Fermion Compounds Organic materials 1 Strongly Correlated Systems: High Temperature Superconductors 2 Superconductivity: