Lecture 1B Superconductivity

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15 Νοε 2013 (πριν από 3 χρόνια και 8 μήνες)

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Superconductivity
One
of the most elegant
phenomenon and beautiful story in
Condensed Matter
Physics
封东来
超导体
有些金属和化合物在降到接近绝对零度时,它
们的
电阻率突然减小到零
,这种现象叫超导
.
0.05
0.10
4.10 4.20 4.30
*
*
*
*
超导的转
变温度
T/K
R/

C
T
汞在
4.2K
附近
电阻
突然
降为

BCS
理论
1980’s
中期,发现“高
温”超导体(化合物超
导电性)
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
Conventional SC:
Phonons mediated
superconductivity
1900 1920 1940 1960 1980 2000
0
20
40
60
80
100
120
140
160
180
Year of Discovery
Transition Temperature (K)
Nb
3
Ge
Nb
3
Sn
NbN
Nb
Pb
Hg
BCS Theory
C60
MgB2
History of Superconductivity
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
Instinct !
H. Kamarligh Onnes and Tuyn. Leiden Commun No.160 (1922)
"to trace a possible difference in the vanishing point (of resistivity) of
Pb and Uranium Pb (Pb-206 isotope). Regarding a difference of
vanishing point temperature for isotopes, it seemed not impossible
that the occurrence of the superconductivity might be influenced the
mass of the nucleus"
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
HTSC:
New mechanism?
Conventional SC:
Phonons mediated
superconductivity
1900 1920 1940 1960 1980 2000
0
20
40
60
80
100
120
140
160
180
Year of Discovery
Transition Temperature (K)
Nb
3
Ge
Nb
3
Sn
NbN
Nb
Pb
Hg
BCS Theory
C60
MgB2
History of Superconductivity
Hg-Ba-Ca-Cu-O
Tl-Ba-Ca-Cu-O
Bi-Sr-Ca-Cu-O
Y-Ba-Cu-O
La-Ba-Cu-O
Hg-Ba-Ca-Cu-O (pressure)
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
4
He
3
He
Lev D. Landau
Pyotr L. Kapitsa
David M. Lee Douglas D. Osheroff Robert C. Richardson
Anthony Leggett
Superfluidity
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
H. Kamerlingh Onnes John Bardeen Leon N. Cooper J. Robert Schrieffer
Ivar Giaever Brian D. Josephson Alexei Abrikosov Vitaly Ginsburg
Superconductivity
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
Deep concepts in superconductivity
- C.N. Yang: Off-diagonal-long-range-order
- P.W. Anderson: Spontaneous symmetry breaking
- Landau-Ginzburg: order parameter
1
. pairing
superconducting gap
2. phase coherence
superfluid
density
Two essential ingredients
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
Classical Rigidity
From Steven M. Girvin, Indiana University
Boulder school 2000 lecture notes
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
Generalized rigidity in superconductor
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
"Generalized Rigidity"
(Anderson, 1960's)
Atoms displaced ->
"Super-flow" of momentum
N S
Superflow of charge.
Electron phase displaced ->
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
Microscopic order produce rigidity
1934, Garter & Casmir "two-
fluid' model
But Order-parameter is a
complex one, not a scalar
It is the complex pair wave
function (BCS 1957)
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
Rigidity explains Meissner effect
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
BCS theory
e
+Z +Z
+Z
+Z
e
PHONON MEDIATED PAIRING
Pairs of electrons: Cooper pairs
T
c
~
ω
ph
exp(-1/
λ
)~M
-1/2
El-ph coupling constant:
λ
Superconducting gap:

Superconductivity: condensation of Cooper pairs
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
Superconductivity
2-electron
bound state
-k
k
Cooper Pair
spin-singlet pairing
Superconductivity can only
be seen on low energy scales
and needs high resolution
!
Metallic Density of States
Superconducting Density of States
Classic low temperature superconductor
A. Chainani et al., PRL 85 (2000)
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
22
-0.4 -0.3 -0.2 -0.1 0 0.1 0.2
Energy Relative to the Fermi Level (eV)
Bi2212
Tc = 78K
--- 20 K
--- 85 K
A
B
Γ
Y
M
A
B
M
Photoemission Intensity
(π, 0)

s-wave”

d-wave”
A
A
B
B
Courtesy of Kyle Shen
High temperature Superconductor
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
BCS quasiparticle in electron spectroscopy
Campuzano et al. PRBn (1996)
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
Current superconductivity research field

Organic
superconductor

Heavy
Fermion
superconductor

High
Tc
Superconductor

Ruthenate
superconductor

Vortex

MgB2

Applications
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
25
Cu d
x
2
-y
2
highest occupied orbital
CuO
Block-
layers
La/Sr
O
Cu
La
2-
ξ
Sr
δ
CuO
4
Unusual normal state
•Pseudogap
Unusual superconducting state
•Anisotropic d-wave gap
Structure and Phase diagram
Heavy
Fermion
superconductors
Phase diagram of
Heavy Fermion system CePd
2
Si
2
Mathur et al.,
Nature 394, 39 (1998)
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
RuO
2
SrO
SrO
Layered
perovskite
Spontaneous
magnetic fields
G.M. Luke et al., Nature 394, 558 (1998)
Maeno et al., Nature 372, 532 (1994)
Unconventional
superconductivity
spin-triplet pairing
Superconductivity
T
C
=1.5 K
µ
SR
-k
k
Cooper Pair
BCS
spin-singlet

Pairing mechanism?
• Order parameter?
• Magnetic fluctuations?
Sr
2
RuO
4
: why is it interesting?
CDW/Superconductor coexistence
E. Morosan et al., Nat. Phys. 2, 544 (2006)
Newly High Tc Iron-Based
Layered Superconductor
The first discovered Iron-based superconductor--LaOFeP
Tc:
Pure LaOFeP – 4K
F doped –7K
Y. Kamihara et al, J. Am. Chem. Soc. 128, 10012 (2006)
Enhancement of Tc (~26K): La[O
1-x
F
x
]FeAs (x=0.05-0.12)
Y. Kamihara et al, J. Am. Chem. Soc. 130, 3296 (2008)
Superconductivity at 43 K in SmO
1−x
F
x
FeAs
X. H. Chen et al, cond-mat/0803.3603v1
Annealed @ 1160 C
Annealed @ 1200 C
Fresh gap data on iron
-
based sc.
Donglai Feng “Electronic Structure of Strongly Correlated Systems”
Try your luck!
THANK YOU!