100 years of Superconductivity: achievements and delusions

100 years of
Superconductivity:
achievements and delusions
A.A.Varlamov
Institute of Superconductivity
and Innovative Materials
SPIN-CNR, Italy

1911: discovery of superconductivity
Discovered by Kamerlingh Onnes
in 1911 during first low temperature
measurements to liquefy helium
Whilst measuring the resistivity of
pure Hg he noticed that the
electrical resistance dropped to zero at
4.2K
In 1912 he found that the resistive
state is restored in a magnetic field or
at high transport currents
1913

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

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

1935: Brothers London theory
H
H=0

Superconductivity in alloys
Lev Shubnikov with coauthors studied superconductivity in metallic
alloys Pb-Tl, 1935. J.N. Rjabinin and L.W. Schubnikow. Nature London,
135 (1935), p. 581.

1937 USSR: Instead of Nobel
Prize – Death Penalty!
Lev Shubnikov

Superconductivity in binary alloys

1937: Superfluidity of liquid He 4
1978

Landau theory of 2 nd order phase transitions
Order parameter? Hint: wave function of Bose condensate
(complex!)
1962

1950: Ginzburg-Landau
Phenomenology Ψ-Theory of
Superconductivity
Order parameter? Hint: wave function of Bose condensate
(complex!)
Inserting
and using the energy conservation law
2003
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

Thus the Gibbs free energy acquires the form
Ginzburg-Landau functional
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: Herbert Fröhlich arrives to the idea
of electron phonon attraction

1957: Discovery of the type II
superconductivity
2003

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)

1957: BCS- Microscopic theory of
superconductivity
$L
1972

!
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.

Extensions of the BCS theory:
I. 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:
" = #e i$
supercurrent

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

II. BCS Superconductivity: long-range order
3D case
" = #e i$
In superconducting state
!
"( r)" ( r' ) = & 2
|r#r'|$%
In normal state, due to fluctuations
" = 0
!
Due to fluctuations:
!
"( r)" ( r' ) = & 2 #|r#r'|
e
'
|r#r'|$%

2D Superconductivity: Wegner - Mermin - Hohenberg
theorem (1968): destruction of the long-range order
by the phase fluctuations
"( r)" ( r' ) |r#r'|$%
~
&
ik r#r'
e ( ) d 2 k
( )
Dk 2 + T #T c
~ ln | r # r'|
' GL
T ( )
1972-1973: Berezinsky–Kosterlitz–Thouless transition
( )
$
F = E "TS = #n s2
T
&
% 2m
" 2k T
'
B ) ln R ( a
!
"( r)" r'
( ) |r#r'|$%
~ )
| r # r'|
& GL ( T )
'
(
*
,
+
# mT
-n s

1962: Josephson effect
Amplitude
S
S
1973

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

Weak superconductivity in Italy
Arco Felice-Naples-Salerno
Since 70-ies is the world
recognized center of
research and applications
of a weak
superconductivity

1986: Discovery of the High Temperature
Superconductivity in Oxides
Superconducting ceramics BaPbO with Tc=10 K
Where discovered in 70-es
LaBaCuO 4 : T c =35 K
1987
Chaplygin et al, 1980
IGNC, RAS, Russia
B. Raveau, France, 1984

1987: YBa 2 Cu 3 O 6+x àT c =93 K
Nitrogen limit id overpassed!

1988: Superconductivity in BSCCO
Bi-2201 has T c ≈ 20 K, Bi-2212 has T c ≈ 95 K, Bi-2223 has T c ≈ 108 K, and Bi-2234 has T c ≈ 104K.
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£l.fi. VLL
60
Bi2.2Sr2Cao.SCU20S+S
40
20
E
0 u
0.5
.0
co
Q.
0.4
____..-£ ......
o
'T
J HII a,b
o
o 0 0
12 5 HII a.b OT
o
o
o
o
H..la,b 12
o
g
o 0
2T 0 0 0
• 0 0 8
• 0 0
0.3
o
0.2
g
: g 8
J g g ;
0.1
. DO
• : 0 0 0
'.l r :Ii
o°..p0
Ii 00
..,.._...
0.0
L
... · •.
0 20 40 60 80 100
T(K)
Fig. 6.49. Magnetic field dependence of the in p lane electrical rcsh-itivil v li jj /,! I
at the superconducting phase transition of single crystalline Bi-22 12 . Nql,' II II
difference in the features, depending on the orientation of tlw f'x t ('III:d 11, 1,1
lower frame ernphasizes the low resistance regime (see Ref.[IGS])
f I

1992: Superconductivity in fullerides
1)A 3 C 60 (A = K, Rb, Cs or some combination of these
elements,
2) Na 2 A x C 60 (x ≤ 1) ( A = K, Rb, Cs or a combination of
these elements,
3) A 3−x Ba x C 60 (A=K, Rb, Cs), 4) Ca x C 60 (x ∼ 5) and Ba 6 C 60

2001:Two band superconductor: MgB 2

Anomalies of HTS
Growth of c-axis resistance
Non-BCS behavior of Hc2
Giant Nernst effect
Existing of pseudogap above Tc
d-symmetry of the order parameter

ARPES experiments: reconstraction of the Fermi
surface by means of energy resolved
photoemission

Is antiferromagnetism related to
superconductivity?
3. Parent compounds are Mott insulators
and Heisenberg antiferromagnets
superconductor

Can we think about spin fluctuations as a new pairing glue?
!(k) = -
"
V spin
(q) ! (k + q) dq
V spin
(q)
>
0,
repulsive,
peaked at q
=
( π , π )
+
0
0
−
−
0
0
Campuzano + et al
d-wave

2006: Fe-Pnictide high temperature
Binary componds of pnictogens.
A pnictogen – an element from
the nitrogen group N,P, As,Sb,Bi
superconductors
RFeAsO (1111)
R = La, Nd, Sm, Pr, Gd
LaOFeP
AFe2As2 (122)
A = Ba, Sr, Ca
LiFeAs (111)
Fe(Se/Te) (11)

Hole Fermi
surface
Band theory calcula/ons agree with experiments
Lebegue, Mazin et al, Singh & Du, Cvetkovic & Tesanovic…
Electron
Fermi surface
2 circular hole pockets around (0,0)
2 elliptical electron pockets around (π,π) (folded BZ), or (0,π)
and (π,0) (unfolded BZ)

T c (K)
SmFeAsO 1-x
Gd 1-x Th x FeAsO
SmFeAsO 1-x F x
PrFeAsO 1-x F x
NdFeAsO 1-x F x
SmFeAsO 1-x F x
CeFeAsO 1-x F x
GdFeAsO 1-x F x
GdFeAsO 1-x
Tb 1-x Th x FeAsO
TbFeAsO 1-x F x
DyFeAsO 1-x F x
Ba 1-x K x Fe 2 As 2
Sr 1-x K x Fe 2 As 2
Eu 1-x K x Fe 2 As 2
LaFeAsO 1-x F x
La 1-x Sr x FeAsO
Ca 1-x Na x Fe 2 As 2
Eu 1-x La x Fe 2 As 2
Li 1-x FeAs
BaCo x Fe 2-x As 2
SrCo x Fe 2-x As 2
BaNi x Fe 2-x As 2
FeSe 0.5 Te 0.5
LaO 1-x F x FeP
LaOFeP
LaONiP
BaNi 2 P 2
LaO 1-x NiBi
α-FeSe 1-x
SrNi 2 As 2
α-FeSe
2008
courtesy of J. Hoffman

Cuprates
Pnictides
Parent compounds are insulators
Parent compounds are metals

How about using the “analogy” with the cuprates and
assume that the pairing is mediated by spin fluctuations
Cuprates
spin fluct.
+
Fe-pnictides
−
0
−
+
spin fluct.
Δ ( θ ) = Δ 0
(cos k
x
- cos k
y)
+
Δ
−
( k = 0) = Δ
Δ
0,
Δ ( k = π,
π ) = -
0
d-wave gap (d x2-y2 )
sign-changing s-wave gap (s +- )

HTS and its applications
American Superconductor Corporation

MAGLEV: flying train
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.

Superconducting RF cavities for colliders

Energy transmission

Transformers for railway power supply

Powerful superconducting magnets

Scientific and industrial NMR
facilities
900 MHz superconductive
NMR 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