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Superconductivity: approaching the century
jubilee
Andrey Varlamov Institute of Superconductivity
and Innovative Materials (SPIN) CNR, Italy
2nd International School on Nanophotonics and Photovoltaics
Zakhadzor 15-22 September 2010
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
The superconducting elementsLi Be
0.026B C N O F Ne
Na Mg Al1.1410
Si P S Cl Ar
K Ca Sc Ti0.3910
V5.38142
Cr Mn Fe Co Ni Cu Zn0.875
5.3
Ga1.091
5.1
Ge As Se Br Kr
Rb Sr Y Zr0.546
4.7
Nb9.5198
Mo0.929.5
Tc7.77141
Ru0.51
7
Rh0.03
5
Pd Ag Cd0.56
3
In3.429.3
Sn3.7230
Sb Te I Xe
Cs Ba La6.0110
Hf0.12
Ta4.483
83
W0.012
0.1
Re1.420
Os0.65516.5
Ir0.141.9
Pt Au Hg4.153
41
Tl2.3917
Pb7.1980
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=9KHc=0.2T
Fe(iron)Tc=1K
(at 20GPa)
Fe(iron)Tc=1K
(at 20GPa)
...or so we thought until 2001
Landau theory of 2nd order phase transitionsOrder parameter? Hint: wave function of Bose
condensate (complex!)
19131913
1950: Ginzburg-Landau Phenomenology Ψ-Theory
of SuperconductivityOrder 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
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.
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.
U. Essmann and H. TraubleMax-Planck Institute, Stuttgart Physics Letters 24A, 526 (1967)
Magneto-optical image of Vortex lattice, 2001P.E. Goa et al.University of OsloSupercond. Sci. Technol. 14, 729 (2001)
Scanning SQUID Microscopy of half-integer vortex, 1996J. R. Kirtley et al. IBM Thomas J. Watson Research CenterPhys. Rev. Lett. 76, 1336 (1996)
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
Scientific and industrial NMR facilities
900 MHz superconductiveNMR installation. It is used For pharmacological investigations of various bio-macromolecules. Yokohama City University
Fluctuation Phenomena in Fluctuation Phenomena in SuperconductorsSuperconductors
2nd International School on Nanophotonics and Photovoltaics
Zakhadzor 15-22 September 2010
Andrey VarlamovInstitute of Superconductivity and Innovative
Materials (SPIN), CNR, Italy
Fluctuation thermodynamical
potential
Green function
Diagrammatic presentation of the fluctuation corrections
Fluctuation correction the
Green function
Temperature dependence of the FC at different fields close to H_{c2}(0) and comparison to experimental data for thin films of LaSCO with T_{c0}≈19K and
B_{c2}(0)≈15T