M. Gabay
School on modern topics in Condensed matterSingapore, 28/01 – 8/02 2013
Superconductivity: background
Paris :January
20th, 2013
The waterwell on the
Butte aux Cailles,
Paris
o So, what’s new about superconductivity?
o It takes two (lengthscales) to tango.
o Thermo-electro-dynamics within BCS s-wave.
o Tc physics: Landau-Ginzburg . Mean field works!
o Field effects : one, two, infinity and beyond.
o 2D world. Berezinskii-Kosterlitz-Thouless rocks!
o Disorder : from mild to hot.
o Non s-wave symmetries : cuprates (d), ruthenates (p).
Back to the future surfboard… 30/06/2011
Levitating grad. student…Courtesy PVII
Superconductivity goingstrong1911 2011
-
G
Tight Binding Cooper Pair
Ñ/t Ñ/
vF vF
a~vF x~vF
t
x= Ñ vF/
(j=rv)*
m0
rlL
From (electro)dynamics to thermodynamics
B=mH
lim Pnn/q2 =1/mq0
1/m01/0 !
Normal state Superconducting state
c=-1
fen – fes ~ ½ (N(EF)D)D
m0Hc~F0/lLx~ 2.07 10-15 Tm2
x= Ñ vF/
(T=0)
Pairing glue:e-phonon
Tc is not proportional to nS
(s-wave)
at T=0,
Eª ek-eF
Probing quasiparticle excitations
1/T1T (~ N(0)2)
Hebel-Schlichter
Near Tc
For T<Tc
ns
Critical fluctuations near Tc?
Ginzburg criterion:
~ (kBTc/EF)4~10-12
Hardly any!!
Fluctuations above Tc
Gaussian fluctuations(Aslamasov-Larkin)
Magneto-resistance fluctuations
N. Reyren et al.,Science 317, 1196 (2007).
Magnetic field effects
k has only little T dependenceo k<0.71 ï type I superconductor (H<Hc)o k>0.71 ï type II superconductoro disorder promotes type II
H<Hc1 ï no vortexH>Hc2 ï no superconductorHc1<H<Hc2 ï mixed (vortex) state
m0
m0
Type II superconductor
(Not so) exotic effects
Pauli limit (spin at play)
Vortex physics in low dimensions
d
2D =lL2/ d
B
Ev~(0/4π)2/m0D (~m0Hc2x2d)
Large, so type II Small, so Hc1~0
ï Field induced state for « any » Hï Anisotropy of parallel vs perpendicular field effects
At low T
TBKT/Tc=(1+0.173Rs/(ђ/e2))‐1
Thermal vortex excitations î 1/ 2D 1/ 2D
TBKT/Tc=(1+0.173Rs/(ħ/e2))‐1
Vortex fugacity
y(TBKT)= exp‐Tc/TBKT~1
Vortex- Antivortex interaction:
E(V-AV)~(0/4)2/em02DLn r
2D(T) = 2D/(1-T/Tc))
BKT transition
Pair entropy:
S~ 2kBLn r
DF=E-TS changes sign at TBKT:
T>TBKT normal state (free vortices)T< TBKT superconducting state
TBKT μ « ns »such that K=2/p
K= 0/4)2/em02D
If e~1,
BUT
+ ‐
2pkBTK/r
jF0j Magnus
Interactions
Free vortices, when the two forces are equal (r=r*)
Flux flow resistance R~ nV ~ exp‐pKLn r* ~ j pK
2D Superconductivity at the LAO/STO Interface
185 190 195 200 2050
50
100
150
150 200 250 3000
2
4
6
8
10-8 10-7 10-610-7
10-6
10-5
10-4
10-3
(dln
(R)/d
T)-2
/3 (
K2/3 )
T (mK)
TBKT=190mK
a
T (mK)
TBKT=188mK
180
185187
190195
200
Volta
ge (V
)
Current (A)
V Iaa(TBKT) = 3
N. Reyren et al, Science 317, 1196 (2007)Finite size effect
R exp(‐ct –1/2)t=1-TBKT/T
Disorder effects
Mild consequences of scattering on non magnetic impurities
Anderson theorem : Tc does not change (s-wave)
x 2=Dt , D=1/d l vF , xpure=vFt
Maki-Thompson-Larkin
Severe consequences of scattering on magnetic impurities
Abrikosov-Gorkov
Severe consequences of scattering in 2d, for Rs=h/4e2
Superconductor-insulator transition
Ñ/t = nN(0)S(S+1)!|u|2dW
A.D. Caviglia, S. Gariglio, N. Reyren, D. Jaccard, T. Schneider, M. Gabay, S. Thiel, G. Hammerl, J. Mannhart, J.-M. Triscone, Nature 456, 624 (2008 )
Large local coulomb repulsion:d-wave superconductivity
OK
Bad
Disorder effects
For non s-wave symmetry, disorder is always bad
S.V. Borisenko, 05‐2011 Phys. Rev. Lett. 105, 136401 (2010)
p-wave symmetry
SRO M-M RMP 2003