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