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

Superconductivity in alloys

1933: Meissner-Ochsenfeld effect

Ideal conductor! Ideal diamagnetic!

1935: Brothers London theory

H

H=0

1937: Superfluidity of liquid He4

19131913

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.

1950: Isotopic effect

1950:Electron phonon attraction

L

1957: BCS- Microscopic theory of superconductivity

19721972

1957: Discovery of the type II superconductivity

20032003

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)

1986: Discovery of the High Temperature Superconductivity in Oxides

19871987

1987: Nitrogen limit is overpassed

YBa2Cu3O7-x: Tc=93 K

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

Superconducting RF cavities for colliders

Energy transmission

Transformers for railway power supply

Powerful superconducting magnets

Scientific and industrial NMR facilities

900 MHz superconductiveNMR installation. It is used For pharmacological investigations of various bio-macromolecules. Yokohama City University

Medical NMR tomography equipment

Criogenic high frequency filters for wireless communications

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

Smearing of the transition

0D super-conductor

In-plane resistance of HTS

Transversal resistance of HTS

Nernst effect in cuprates

Superconducting fluctuations near Tc: qualitative picture

Ginzburg-Landau formalism

Fast (fermionic) and slow (bosonic) variables

Quadratic GL approximation

( ) exp( )k

k

r ikr

d

ξ(T)

0D

Exact solution for the 0D superconductor

Microscopic theory of fluctuations

Fluctuation propagator

Fluctuation thermodynamical

potential

Green function

Diagrammatic presentation of the fluctuation corrections

Fluctuation correction the

Green function

Leading-order fluctuation propagator contributions

to the electromagnetic response operator

Aslamazov-Larkin paraconductivity

~

When T=0

When T>>Tc

When T-Tc<<Tc

=

=

Anomalous MT contribution

~

When T-Tc<<Tc

When T=0

Density of States Renormalization

Δσ(2)DOS= - 0.1e2/ħ ln(1/ε)When T-Tc<<Tc

When T=0 -

Diffusion coefficient renormalization

Δσ(2)DOS= - 0.1e2/ħ ln(1/ε)

When T-Tc<<Tc

When T=0

Exact solution

Asymptotic regimes in the phase diagram

Fluctuation conductivity surface as the function of temperature and

magnetic field

Contours of constant fluctuation conductivity.

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

Quantum fluctuations near Hc2(0): qualitative picture

~

Close to Tc:

Close to Hc2(0):

Snapshot visible for times shorter than τQF