physics

1. Superconductivity: approaching
the century jubilee

2. 1911: discovery of superconductivity
Whilst measuring the resistivity of
“pure” Hg he noticed that the electrical
resistance dropped to zero at 4.2K
Discovered by Kamerlingh Onnes
in 1911 during first low temperature
measurements to liquefy helium
In 1912 he found that the resistive
state is restored in a magnetic field or
at high transport currents
19131913

5. The superconducting elements
Li Be
0.026
B C N O F Ne
Na Mg Al
1.14
10
Si P S Cl Ar
K Ca Sc Ti
0.39
10
V
5.38
142
Cr Mn Fe Co Ni Cu Zn
0.875
5.3
Ga
1.091
5.1
Ge As Se Br Kr
Rb Sr Y Zr
0.546
4.7
Nb
9.5
198
Mo
0.92
9.5
Tc
7.77
141
Ru
0.51
7
Rh
0.03
5
Pd Ag Cd
0.56
3
In
3.4
29.3
Sn
3.72
30
Sb Te I Xe
Cs Ba La
6.0
110
Hf
0.12
Ta
4.483
83
W
0.012
0.1
Re
1.4
20
Os
0.655
16.5
Ir
0.14
1.9
Pt Au Hg
4.153
41
Tl
2.39
17
Pb
7.19
80
Bi Po At Rn
Transition temperatures (K)
Critical magnetic fields at absolute zero (mT)
Transition temperatures (K) and critical fields are generally low
Metals with the highest conductivities are not superconductors
The magnetic 3d elements are not superconducting
Nb
(Niobium)
Tc=9K
Hc=0.2T
Fe
(iron)
Tc=1K
(at 20GPa)
Fe
(iron)
Tc=1K
(at 20GPa)
...or so we thought until 2001

6. Li Be
0.026
B C N O F Ne
Na Mg Al
1.14
10
Si P S Cl Ar
K Ca Sc Ti
0.39
10
V
5.38
142
Cr Mn Fe Co Ni Cu Zn
0.875
5.3
Ga
1.091
5.1
Ge As Se Br Kr
Rb Sr Y Zr
0.546
4.7
Nb
9.5
198
Mo
0.92
9.5
Tc
7.77
141
Ru
0.51
7
Rh
0.03
5
Pd Ag Cd
0.56
3
In
3.4
29.3
Sn
3.72
30
Sb Te I Xe
Cs Ba La
6.0
110
Hf
0.12
Ta
4.483
83
W
0.012
0.1
Re
1.4
20
Os
0.655
16.5
Ir
0.14
1.9
Pt Au Hg
4.153
41
Tl
2.39
17
Pb
7.19
80
Bi Po At Rn
Transition temperatures (K)
Critical magnetic fields at absolute zero (mT)
Li
(Lithium)
Tc<0.4mK
Li
(Lithium)
Tc<0.4mK
Helsinki University of Technology
Low Temperature Laboratory, 2007

7. Superconductivity in alloys

8. 1933: Meissner-Ochsenfeld effect
Ideal conductor! Ideal diamagnetic!

10. 1935: Brothers London theory
H
H=0

11. 1937: Superfluidity of liquid He4
19131913

12. Landau theory of 2nd
order phase transitions
Order parameter? Hint: wave function of Bose condensate
(complex!)
19621962

13. 1950: Ginzburg-Landau
Phenomenology Ψ-Theory of
Superconductivity
Order parameter? Hint: wave function of Bose condensate
(complex!)
Inserting and using the energy conservation law
How one can describe an inhomogeneous state?
One could think about adding . However, electrons
are charged, and one has to add a gauge-invariant
combination
20032003

14. Ginzburg-Landau functional
Thus the Gibbs free energy acquires the form
To find distributions of the order parameter Ψ and
vector–potential A one has to minimize this functional
with respect to these quantities, i. e. calculate variational
derivatives and equate them to 0.

15. Minimizing with respect to
Minimizing with respect to A:
Maxwell equation
The expression for the current indicates that the
order parameter has a physical meaning of the
wave function of the superconducting condensate.

16. 1950: Isotopic effect

17. 1950:Electron phonon attraction

18. 1957: Discovery of the type II
superconductivity
20032003

19. U. Essmann and H. Trauble
Max-Planck Institute, Stuttgart
Physics Letters 24A, 526 (1967)
Magneto-optical image
of Vortex lattice, 2001
P.E. Goa et al.
University of Oslo
Supercond. Sci. Technol. 14, 729 (2001)
Scanning SQUID Microscopy of half-integer vortex, 1996
J. R. Kirtley et al. IBM Thomas J. Watson Research Center
Phys. Rev. Lett. 76, 1336 (1996)

20. $L
1957: BCS- Microscopic theory of
superconductivity
19721972

21. 1958: Lev Gorkov
formulates elegant equations of the
microscopic theory of superconductivity
and demonstrates the equivalence
between the microscopic BCS theory
and GL phenomenology at
temperatures close to the critical one.

22. Extensions of the BCS theory

23. BCS Superconductivity: no gap – no supercurrent!
The order parameter Ψ has a physical meaning of
the wave function of the superconducting
condensate and the gap in the quasi-particle
spectrum determines its modulus:
Ψ=∆eiφ
supercurrent

24. 1959: Abrikosov & Gorkov: Gapless Superconductivity
0.915ccr<c<ccr
there is no gap but supercurrent exists
In the interval of concentrations
Superconductor with paramagnetic impurities

25. BCS Superconductivity: long-range order
Ψ=∆eiφ
Ψr()Ψr'()|r−r'|→∞
=∆2
In superconducting state
In normal state, due to fluctuations
Ψr()Ψr'()|r−r'|→∞
=∆2
e
−
|r−r'|
ξ
3D case
Ψ=0
Due to fluctuations:

26. 2D Superconductivity: Wegner - Mermin - Hohenberg
theorem (1968): destruction of the long-range order
by the phase fluctuations
Ψr()Ψr'()|r−r'|→∞
~
eikr−r'( )
d2
k
Dk2
+T−Tc( )∫ ~ln
|r−r'|
ξGLT()
1972-1973: Berezinsky–Kosterlitz–Thouless transition
Ψr()Ψr'( )|r−r'|→∞
~
|r−r'|
ξGL T( )






−
mT
πns
F=E−TS=
πns2T()
2m
−2kBT





ln
R
a

27. 1973: Superfluidity in liquid He3
David M. Lee, Douglas Dean
Osheroff and Robert C. Richardson
19961996 20032003
Antony Legget

28. Superconductivity with nontrivial
symmetry of the order parameter:
Kirtley: Phase sensitive pairing symmetry tests. Observation of thehalf-flux quantum
effect in a tricrystal geometry, showed that the gap has predominantly d-wave symmetry
in a number of the cuprate high-Tc superconductors

29. 1962: Josephson effect
S S
Amplitude
19731973

31. Link
Since the energy gain depends on the phase difference,
the finite phase difference must create persistent current
transferring Cooper pairs between the leads

32. 1986: Discovery of the High Temperature
Superconductivity in Oxides
19871987

33. 1987: Nitrogen limit is overpassed
YBa2Cu3O7-x: Tc=93 K

35. Two band superconductor: MgB2

36. The linear motor car experiment vehicles MLX01-01 of Central Japan Railway
Company. The technology has the potential to exceed 4000 mph (6437 km/h) if
deployed in an evacuated tunnel.
MAGLEV: flying train

37. Superconducting RF cavities for colliders

38. Energy transmission

39. Transformers for railway power supply

40. Powerful superconducting magnets

41. Scientific and industrial NMR facilities
900 MHz superconductive
NMR installation. It is used
For pharmacological
investigations of various
bio-macromolecules.
Yokohama City University

42. Medical NMR tomography equipment

43. Criogenic high frequency filters
for wireless communications