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
3.
4.
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
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.
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)
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.
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
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
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
41. Scientific and industrial NMR facilities
900 MHz superconductive
NMR installation. It is used
For pharmacological
investigations of various
bio-macromolecules.
Yokohama City University
