Electronic Raman scattering in high Tc cuprate ...€¦ · Electronic Raman scattering in high Tc cuprate superconductors Toward an understanding of the phase diagram Courtesy: M

Electronic Raman scatteringin high Tc cuprate superconductors

Toward an understanding of the phase diagram

Courtesy: M. Le Tacon, Squap, MPQ

Alain SacutoLaboratoire Matériaux et Phénomènes Quantiques

Université Paris Diderot-Paris 7

• Density of Cooper pairs and fraction of coherent Fermi Surface: - Do we really need to invoke 2 gaps to explain the 2 energy scales? - How to reconcile transport and spectroscopy measurements: thermal

conductivity, heat capacity

• Exploration of the normal state of cuprates : - electronic Raman response function in the normal state- observation of the pseudo gap state in cuprates

OutlinePart 3

• Exploration of the superconducting state of cuprates- the symmetry of a superconducting gap - the emergence of 2 energy scales in the SC state- the question of one or two gaps ? - the controversy on photo-emission data

• Differences and analogies between cuprates and pnictides superconductors (Yann Gallais)

- introduction to iron pnictides superconductors- superconducting gap symmetry- superconductivty and spin density wave order

• An attempt to give a global view of the cuprate phase diagram

Outline

Part 4

s – wave gap versus d-wave gap

s - wave gap: full gap d- wave gap: nodes

T = 0

..

..... .....

........T ≠ 0below Tcd - wave more excited electrons

only around nodes

Nodes

s-wave few excited electrons

Thermal conductivityNote the exponential drop at low temp

~Tnormal state

Kes 1974

Nb

Yu, PRL 1992

YBC0

Fmv vlTCT )()( ∝κ Fmv vTlTCT )()()( ∝κS-wave d-wave

Tunneling in Al/AlO/Al

From Nobel Prize lecture in 1973

Ivar Giaever 1973

Tunneling experiments Nb vs Cuprates

Pan et al. 1998Renner and Fisher 1998Maggio Aprile 1995

For a review ; See RMP 79, 2007,O. Fischer

Photon in

Photon out

Electron-hole pair created

energy of the excited electron,

Momentum area

Electronic Raman scattering process

Photo-emission (ARPES)

Extraction of one electronenergy of the excited electron

momentum e-

Photon in

Ecxited electronic states from the Fermi sea

Photo emission Spectroscopy

Temperature-dependent photoemission spectra fromoptimally doped Bi-2212 (Tc=91 K), angle integratedover a narrow cut at (π,0). Inset: superconducting-peak intensity vs temperature. After Fedorov et al., 1999.

Coherent peakBogoliubov quasiparticles

Δ

B-i2212

ARPES measurements on Bi-2212

Ding, Norman, et al., 1996 13 K Bi2212

Tc = 87 K

Pt

What is Electronic Raman response?

Mercurate familyTetragonal structure

D. Colson, CEA

Hg-1212Tc=120 K

Hg-1201Tc = 95 K

Hg-1223Tc=135 K

Tc=165 K (30 GPa)

Hg

Ba

Ca

CuO2plane

oxygen

Hg-1201

-108 °C

diamond past polishing (one tenth microns)

Electronic Raman scattering

Polarizations Ei et Es Momentum probe

kx, kx=±ky

Raman shift ωR = ωi -ωs Energy proberesolution < 1 meV

ωi , Ei

Incident

ωs , Es

Scattered

ωRamanLattice

OrElectronic

ExcitationsFermi level

e- holepair

ωR

Raman momentum probe in cuprate structure

γB2gxy

γA1gx2+y2

γA2g→ 0

γB1gx2-y2

Cu

O

x

y

Cu

O

x

y

C

O

x

y

Real space k space

Probe allFermi surface

Probe (π,π)« cold spots »

Probe (π,0)« hot spots »

symmetry

Anti-Nodes

Nodes

T. P. Devereaux, D. Einzel (95)M. V. Klein, S. B. Dierker (84)

0,0 0,5 1,0 1,5 2,00,0

0,5

1,0

1,5

2,0

ω

χ''(ω

) ar

b.un

its

ω/2Δ0

Anti-Nodal Nodal

ΔΑΝ

/ΔΝ =1.2

ω3

Electronic Raman Responsed - wave superconducting gapky

kx

0 200 400 600 8000

1

2

3

χ"(ω

) (ar

b. u

nits

)

Raman Shift (cm-1)0 200 400 600 800

0

1

2

3

Raman Shift (cm-1)0 200 400 600 800

0

1

2

3

Raman Shift (cm-1)0 200 400 600 800

0

1

2

3

Raman Shift (cm-1)0 200 400 600 800

0

1

2

3

Raman Shift (cm-1)0 200 400 600 800

0

1

2

3

Raman Shift (cm-1)

2Δ0

Hg-1201Tc=95KT=12K

AN

N

E

Probing the Superconducting statevs doping, p

0doping level

Tem

pera

ture

Pseudo gapFermi liquid ?

Strangemetal

SC state

AFstate

UD OD

TcM = 95 K

10 K


0doping level

Tem

pera

ture

Pseudo gap Fermi liquid ?

Strangemetal

SC state

AFstate

UD OD

TcM = 95 K

10 K

Raman response in a superconductor

-Δk

+Δk

superconductor

EF

γ

+γ

χ’’(ω)

ω0

2Δk

gap

M. V. Klein, S.B. Dierker PRB 29(84)

( )SF

k

kNAN

kkFNAN

ZN2122

22

4

20 /

,''

,

)(Re),(

Δ−

ΔΛ∝

ω

γ

ωπωχ

Mercurate familyTetragonal structure

D. Colson, CEA

Hg-1212Tc=120 K

Hg-1201Tc = 95 K

Hg-1223Tc=135 K

Tc=165 K (30 GPa)

Hg

Ba

Ca

CuO2plane

oxygen

Hg-1201

-108 °C

Anti-Nodal ResponseIn the superconducting state

Γ

(π,0) (π,π)

B1g

doping decrease

doping decrease

0 200 400 600 800 0 200 400 600 800

407 cm-1

95K 10K

Ov.92 K

90K 10K

Und.89 K

750 cm-1

90K 10K

Und.86 K

513 cm-1

100K 10 K

Opt.95 K

290 cm-1

10K 80K

Ov.70 K

177 cm-1Ov.42 K

10K 45K

χ"(ω

) (a.

u)

10K 80K

Und.78 K

Raman shift (cm -1)

612 cm-1

100K 10K

Und.92 K

670 cm-1

M. Le Tacon Nature Physics

2, 537, 2006

10 K 10 K

M. V. Klein, S. B. Dierker (84)T. P. Devereaux, D. Einzel (95)

0.0 0.5 1.0 1.5 2.00.0

0.5

1.0

1.5

2.0

ω

χ''(ω

) ar

b.un

its

ω/2Δ0

Anti-Nodal Nodal

ΔΑΝ

/ΔΝ =1.2

ω3

Electronic Raman Responsed - wave superconducting gap

ky

kx

AN

N

Γ

(π,0) (π,π)

B2g

0 2 0 0 4 0 0 6 0 0 8 0 0

7 0 K 1 0 K

R a m a n s h if t ( c m -1 )

U n d .6 3 K

2 3 0 c m -1

3 8 0 c m -1

9 0 K 1 0 K

U n d .8 9 K

3 6 0 c m -1

8 0 K 1 0 K

U n d .7 8 K

4 0 0 c m -1

1 0 0 K 1 0 K

O v .9 2 K

3 7 0 c m -1

9 0 K 1 0 K

U n d .8 6 K

2 9 7 c m -1

8 0 K 1 0 K

O v .7 0 K

1 7 0 c m -1

O v .4 2 K

5 0 K 1 0 K

0 2 0 0 4 0 0 6 0 0 8 0 0

5 1 0 c m -1

1 0 0 K 1 0 K

O p t.9 5 K

Nodal ResponseIn the Superconducting state

doping decrease

doping decrease

2 qsp dynamics

10 K 10 K

0.09 0.12 0.15 0.18 0.21 0.24

200

400

600

800

Ene

rgy

(cm

-1)

Doping level p

ΔΑΝ

ΔΝ

Raman Hg-1201

TC

T=10 KT

T

E

p hole doping

T*

Tc

ΩB1g

ΩB2g0

Temperature phase diagramTransport probes

Energy phase diagramSpectroscopic probes

p*

Do not make confusion betweenthe energy and the temperature phase diagram!

G. Gu, BNL, USA

Bi - 2212T maxc= 92 K

Bi

BaCa

Bi-2212 single crystal

0

1

2

0

1

2

0

1

2

0

1

0

1

0

1

0

1

2

3

0

1

0

1

2

0

1

0 200 400 600 8000

1

2

200 400 600 800 0

1

10K 94K

10K 100K

/1 .5

10K 85K

0 .19 TC= 84K

p=0 .21 TC= 75K

0 .1 TC=68K

0 .12 TC=75K

0 .14 TC=87K

0 .16 TC=91K

10K 85K

χ''(ω

,T)

(cts

.s-1.m

W -1

)

B 2g

10K 95K

ω (cm -1) ω (cm -1)

10K 78K

B 1g

0

0

0

0

0 2 0 0 4 0 0 6 0 0 8 0 0

0

2 0 0 4 0 0 6 0 0 8 0 0

0

p = 0 . 1 6

p = 0 . 1 4

p = 0 . 1 2

p = 0 . 1 0

ω ( c m - 1 ) ω ( c m - 1 )

B 2 g

p = 0 . 1 9

B 1 g

2 energy scales in the SC state of UD cuprates

Bi -2212

2 energy scales in the SC state of UD cupratesby ERS

S. Blanc et al. PRB 89 2009W. Guyard et al. PRB 77 2008M. Le Tacon et al. Nat.Phys. 2006

nodal

anti-nodal

0.08 0.12 0.16 0.20 0.240

20

40

60

80

100

T

Two energy scales story

G. Deutscher, Nature 99

Giaever scale

E

Δc eV

Δ

exictation gap

Insulating barriere

EF

first excitedstate

G

« energy range beyond whichthe pair amplitude return to zero »

p

ΔEF

ASJ scale

« energy range wheresingle particle states are Missing »

Δp eV

G

N S

N S

Observations of two energy scales by several techniques

HC: Loram, Tallon , ERS: R.Hackl, Sugai, Le Tacon.. ARPES: Mesot, Tanaka,Kondo/Kaminski, Borisenko, STM: Boyer, Gomes, Hanaguri/Davis…

0 ,0 0 0 ,0 5 0 ,1 0 0 ,1 5 0 ,2 0 0 ,2 50

5

1 0

R am an B 1 g B 2 g H g-1201 B i-2212

Y -123

LS C O A R P E S Tunne l

ωA

N, ω

N /T

cmax

T

“Two Gaps Make a High Temperature Superconductor?”

Huefner, Damacelli Rep. Prog. Phys. 08 A. Millis, Science 314, 1888, 06

1 or 2 gaps ?

U. Chatterjee et al. , Nat. Phys. 2010films: Tc = 33K(UD),80K(OPT)crystals: 69K (UD).

Kondo et. al. Nat. Phys 2009.

Bi-2201 Bi-2212

Arpes in Bi-compounds: no consensus…

2 gaps against 1 gap

La2−xSrxCuO4

Tc = 36 K

X = 0.145

PRL, 101, 2007 M. Shi et al.

La2−xSrxCuO4

X = 0.15

Tc = 37 K

Slightly UDOpt. Doped

PRL 99, 2007, Terashima

Nodes

Anti-Nodes


0doping level

Tem

pera

ture

Pseudo gap Fermi liquid ?

Strangemetal

SC state

AFstate

UD OD

TcMax

10 K

- (ukvk)2 condensation probability of the Cooper Pairs (de Gennes, Super-conductivity of metals and Alloys, 66)

- Σ (ukvk)2 density of Cooper Pairs around EF as a gap is opening (Legett, k Quantum Liquids in Condensed Matter systems, 2006)

Electronic Raman scattering in a Superconductor

vk2

uk2

(ukvk)2

-Δk

+Δk

superconductor

EF

γ

+γχ’’(ω)

ω0

2Δk

∑∝k

kkvu2)(

Raman response function

( ) 22

2

k

k

kk E

dΔ

=∫ ∑ μγπωωχ )(''

( ) )( tanh)('' kk

k

B

k

kk EETk

E 22 2

22

−Δ

⎟⎟⎠

⎞⎜⎜⎝

⎛= ∑ ωδγπωχ μ

22

2

4 )( kkk

k vuE

=Δ

TR qtqtie >+∫

Area of the peak : density of Cooper pairs

χ’’(ω)

ω0

2Δk

∑∝k

kkvu2)(

0

1

2

0

1

2

0

1

2

0

1

0

1

0

1

0

1

2

3

0

1

0

1

2

0

1

0 2 0 0 4 0 0 6 0 0 8 0 00

1

2

2 0 0 4 0 0 6 0 0 8 0 0 0

1

1 0 K 4 0 K 7 0 K 8 4 K 9 4 K

1 0 K 4 0 K 7 0 K 9 1 K 1 0 0 K

/1 .5

1 0 K 4 0 K 6 0 K 7 5 K 8 5 K

p = 0 .1 9 T C = 8 4 K

p = 0 .2 1 T C = 7 5 K

p = 0 .1 T C = 6 8 K

p = 0 .1 2 T C = 7 5 K

p = 0 .1 4 T C = 8 7 K

p = 0 .1 6 T C = 9 1 K

1 0 K 7 5 K 4 0 K 8 5 K 6 0 K

χ''(ω

,T)

(cts

.s-1.m

W -1

)

B 2 g

1 0 K 4 0 K 6 0 K 8 7 K 9 5 K

ω (c m -1 ) ω (c m -1 )

1 0 K 4 0 K 5 5 K 6 8 K 7 8 K

B 1 g

0.0 0.2 0.4 0.6 0.8 1.00.0

0.2

0.4

0.6

0.8

1.0

1.2

T/Tc

B2gB1g

Bi-2212

0.21 0.21 0.19 0.19 0.16 0.16 0.14 0.14 0.12 0.12 0.10

Nor

mal

ized

P

eak

Are

a B1g & B2g peaks

are coherent excitations of the SC state

Temperature dependence of B1g and B2g peaks

Loss of AN coherent superconducting peak

Over-doped

Under-doped

Anti-Nodes

Nodes

Bi-2212

Γ

B1g

Γ

B2g

0

1

2

0

1

2

0

1

2

0

1

0

1

0

1

0

1

2

3

0

1

0

1

2

0

1

0 2 0 0 4 0 0 6 0 0 8 0 00

1

2

2 0 0 4 0 0 6 0 0 8 0 0 0

1

1 0 K 4 0 K 7 0 K 8 4 K 9 4 K

1 0 K 4 0 K 7 0 K 9 1 K 1 0 0 K

/1 .5

1 0 K 4 0 K 6 0 K 7 5 K 8 5 K

p = 0 .1 9 T C = 8 4 K

p = 0 .2 1 T C = 7 5 K

p = 0 .1 T C = 6 8 K

p = 0 .1 2 T C = 7 5 K

p = 0 .1 4 T C = 8 7 K

p = 0 .1 6 T C = 9 1 K

1 0 K 7 5 K 4 0 K 8 5 K 6 0 K

χ''(ω

,T)

(cts

.s-1.m

W -1

)

B 2 g

1 0 K 4 0 K 6 0 K 8 7 K 9 5 K

ω (c m -1 ) ω (c m -1 )

1 0 K 4 0 K 5 5 K 6 8 K 7 8 K

B 1 g

Quantitative Raman measurements- Easily cleaved- Large homogeneous surface (mm2)- Optical constants (ellipsometry)

G. Gu, BNL, USABi-2212

T maxc=92 K

0 200 400 600 8000

2

4

6

8

10

Raman shift in (cm-1)

Ram

an re

spon

se χ

''(ω

) (c

ts/s

.mW

) B2g

293 K 514.52 nm

Bi -2212 UD 68 K

10 distinct spots

Γ

Bi

BaCa

0 200 400 600 8000

2

4

6

8

10

Raman shift in (cm-1)

OPT 91 K sample A OPT 91 K sample B UD 68 K sample C UD 68 K sample D

293K514.52nm

R

aman

resp

onse

χ''(

ω)

(cts

/s.m

W)

Bi-2212

B2g

S. Blanc et al., 09

Change in intensity

less than 5%for two sampleswith the samedoping level

0.04 0.08 0.12 0.16 0.20 0.240

1

2

3

4

5

doping p

ΣB1g

P

eak

Are

a Σ

0 200 400 600 8000 200 400 600 800

0

0

0

00

0

B2god 70

od 84

opt 90

ud 68

100K 18K

χ" (ω

) (c

ts/s

.mW

)

0

0

B1g 100K 18K

ud 68

opt 90

od 84

od 70

Raman Shift (cm-1 )

Loss of coherent AN PeakNodalA-Nodal

0.04 0.08 0.12 0.16 0.20 0.240

1

2

3

4

5

doping p

ΣB1g ΣB2g

P

eak

Are

a Σ

N

A-N

Densityof Cooperpairs

ky

kx

ky

kx

ky

kx

Over-dopedOpt-dopedUnder-doped

Bi-2212

SuperconductivtyIs robust

at the nodes

S. Blanc et al. PRB 80, 094504 Rapid Com. 2009

0 200 400 600 800

B1g

ud 68

opt 90

od 84

od 70

Raman Shift (cm-1 )

J.C.Campuzano, PRL 99 D.L.Feng et al. Science 2000Blanc et al. PRB 80 2009

Loss of coherent Anti-Nodal superconducting peak

A-Nodal

2 energy scales in the SC state of UD cupratesvarying in opposite manners with U-doping

Coherent Bogoliubov quasiparticles arereduced In the A-N region with U-doping

Both are coherent excitations of the SC stateand disapear at Tc

Summary of our experimental findings:

Are you able to explain the 2 energy scalesin a one gap schem?

Ф=45°

Fermi surface

Strongly overdoped

QPSW decrease

Loss of coherent quasi-particles in a one gap schem

0

1

2

3

0 15 30 45 60 75 900.0

0.5

1.0

ΩB2g

ΩB1g

γB2g

Ζ(φ)

.Λ(φ

)2Δ

(Φ) /Δ

0

vΔ ∝ Δmax

single d-wave gap

φ in degrees0 1 2 3

ΩB1g

B1g

ΩB2g

B2g

ω / Δ0

AN

N

QPSW is preserved( )

SFk

kNAN

kkFNAN

ZN2122

22

4

20 /

,''

,

)(Re),(

Δ−

ΔΛ∝

ω

γ

ωπωχ

Ф=45°

Fermi surface

Strongly overdopedWealky underdoped

QPSW decrease


0

1

2

3

0 15 30 45 60 75 900.0

0.5

1.0

ΩB2g

ΩB1g

γB2g

Ζ(φ)

.Λ(φ

)2Δ

(Φ) /Δ

0

vΔ ∝ Δmax

single d-wave gap


ΩB1g

B1g

ΩB2g

B2g

ω / Δ0

0

1

2

3

0 15 30 45 60 75 900.0

0.5

1.0

ΩB1g

ΩB2g

Ζ(φ)

.Λ(φ

)2Δ

(Φ) /Δ

0

γB2g


ΩB1g

ω / Δ0

p=0.16

B1g

ΩB2g

B2g

AN

N


SFk

kNAN

kkFNAN

ZN2122

22

4

20 /

,''

,

)(Re),(

Δ−

ΔΛ∝

ω

γ

ωπωχ

Ф=45°

Fermi surface


Underdoped

QPSW decrease


0

1

2

3

0 15 30 45 60 75 900.0

0.5

1.0

ΩB2g

ΩB1g

γB2g

Ζ(φ)

.Λ(φ

)2Δ

(Φ) /Δ

0

vΔ ∝ Δmax

single d-wave gap


ΩB1g

B1g

ΩB2g

B2g

ω / Δ0

0

1

2

3

0 15 30 45 60 75 900.0

0.5

1.0

ΩB1g

ΩB2g

Ζ(φ)

.Λ(φ

)2Δ

(Φ) /Δ

0

γB2g


ΩB1g

ω / Δ0

p=0.16

B1g

ΩB2g

B2g

0

1

2

3

0 15 30 45 60 75 900.0

0.5

1.0

ΩB1g

ΩB2g

Ζ(φ)

.Λ(φ

)2Δ

(Φ) /Δ

0


ω / Δ0

p=0.16 p=0.12

B1gΩB1g

ΩB2g

B2g

AN

N


SFk

kNAN

kkFNAN

ZN2122

22

4

20 /

,''

,

)(Re),(

Δ−

ΔΛ∝

ω

γ

ωπωχ

Ф=45°

Fermi surface


Underdoped

QPSW decrease


0

1

2

3

0 15 30 45 60 75 900.0

0.5

1.0

ΩB2g

ΩB1g

γB2g

Ζ(φ)

.Λ(φ

)2Δ

(Φ) /Δ

0

vΔ ∝ Δmax

single d-wave gap


ΩB1g

B1g

ΩB2g

B2g

ω / Δ0

0

1

2

3

0 15 30 45 60 75 900.0

0.5

1.0

ΩB1g

ΩB2g

Ζ(φ)

.Λ(φ

)2Δ

(Φ) /Δ

0

γB2g


ΩB1g

ω / Δ0

p=0.16

B1g

ΩB2g

B2g

0

1

2

3

0 15 30 45 60 75 900.0

0.5

1.0

ΩB1g

ΩB2g

Ζ(φ)

.Λ(φ

)2Δ

(Φ) /Δ

0


ω / Δ0

p=0.16 p=0.12

B1gΩB1g

ΩB2g

B2g

Strongly underdoped

0

1

2

3

0 15 30 45 60 75 900.0

0.5

1.0

ΩB2g

ΩB1g

Ζ(φ)

.Λ(φ

)2Δ

(Φ)/Δ

0


ΩB1g

ω / Δ0

p=0.16 p=0.12 p=0.09

B1g

ΩB2g

B2g

AN

N


SFk

kNAN

kkFNAN

ZN2122

22

4

20 /

,''

,

)(Re),(

Δ−

ΔΛ∝

ω

γ

ωπωχ

0 2 0 0 4 0 0 6 0 0 8 0 0

0 .0 5 0 .1 0 0 .1 5 0 .2 0 0 .2 50 .5

1 .0

1 .5

0

B 2 g o d 7 0

o d 8 4

o p t 9 0

u d 6 8

0

0

0

1 0 0 K 1 8 K

χ"

(ω)

(cou

nts

s-1 m

W-1

)

2

4

6

8

a B i-2 2 1 2

R a m a n s h if t (c m -1)

d o p in g p

αp/α

p-op

t

Cstev

Z N ≈Λ∝Δ

2)(α

in the doping Range of p ~0.1 - 0.16

Doping Evolution of the Slope of the B2g peak

S. Blanc et al. PRB 80, 094504 Rapid Com. 2009

Ф=45°

Fermi surface

Strongly overdopedWeakly underdoped

Underdoped

decrease QPSW preserved QPSW


0

1

2

3

0 15 30 45 60 75 900.0

0.5

1.0

ΩB2g

ΩB1g

γB2g

Ζ(φ)

.Λ(φ

)2Δ

(Φ) /Δ

0

vΔ ∝ Δmax

single d-wave gap


ΩB1g

B1g

ΩB2g

B2g

ω / Δ0

0

1

2

3

0 15 30 45 60 75 900.0

0.5

1.0

ΩB1g

ΩB2g

Ζ(φ)

.Λ(φ

)2Δ

(Φ)/Δ

0

γB2g


ΩB1g

ω / Δ0

p=0.16

B1g

ΩB2g

B2g

0

1

2

3

0 15 30 45 60 75 900.0

0.5

1.0

ΩB1g

ΩB2g

Ζ(φ)

.Λ(φ

)2Δ

(Φ)/Δ

0


ω / Δ0

p=0.16 p=0.12

B1gΩB1g

ΩB2g

B2g

Strongly underdoped

0

1

2

3

0 15 30 45 60 75 900.0

0.5

1.0

ΩB2g

ΩB1g

Ζ(φ)

.Λ(φ

)2Δ

(Φ)/Δ

0


ΩB1g

ω / Δ0

p=0.16 p=0.12 p=0.09

B1g

ΩB2g

B2g

ANN

0.04 0.08 0.12 0.160

20

40

60

fcERS v

Δ ∝ Δmax (Blanc et al.)

hole doping p

f c (in

%)

Fractions of coherent Fermi surface

0.04 0.08 0.12 0.160

20

40

60

fc vΔ ∝ Δmax (Blanc et al.)

f Arpesc (Kanigel et al.)

hole doping p

f c (in

%)

0.04 0.08 0.12 0.160

20

40

60

f c (in

%)

hole doping p

fc vΔ ∝ Δmax (Blanc et al.)

f Arpesc (Kanigel et al.)

f HCc (H.H.Wen et al.)

maxΔ∝ ccB fTk

, cBgB Tk∝Ω 2h

Δ∝Ω vfcgB2h

0

1

2

ΩB2g

2Δ(Φ

)/Δ0

fc

vΔ

maxΔ∝Δv

S. Blanc et al.Phys. Rev. B 82, 144516 (2010)

Antinodal quasi-particles

H. Ding in PRL 2001

« the so called Coherent and Excitation gaps »only one gap in reality

G. Deutscher, Nature 99

Giaever scale

E

p

Δc eV

Δ

Pair BreakingPeak energy

Insulating barriere

EF

G

first excitedstate

ΔEF

ξ

Δp eV

G energy range on whichthe Cooper pairs flow

energy range wheresingle particle states are missing

ASJ scale

B1g

B2gfc

Fractions of FS and a single d-wave gap

p= 0.09

ΩB1g

kY

kX

Fermi Surface at T=TC

ΩB2g

p= 0.16

Energy of the SC gap

-2 -1 0 1 2

dI/d

V

Voltage/Δ0

p=0.16 p=0.14 p=0.12 p=0.11 p=0.09

ANN

FSF

ieVieVZN

dVdI

)()(Re)(

φφ 22 Δ−Γ−

Γ−∝

K. McElroy et al PRL 2005

T

CONCLUSION

Fraction of coherent Fermi Surface

- explains the existence of the 2 energy scalesin the SC state

- controls Tc such as Tc ∝ fc.Δm

- Consistent with : Raman, « Arpes », Tunnelingand transport measurements

AFMott

insulator

Hole doping

Tem

pera

ture

0 p0.05 0.16 0.27

TN

PseudoGap

T*

strange Metalρ∝T

p*

Cuprates phase diagram hole doped

TC

2 distinct regimesIn the SC states

d-wavesuperconductor


AFMott

insulator

Hole doping

Tem

pera

ture

0 p0.05 0.16 0.27

TNT*

p*

Tc

2scales

1scale



AFMott

insulator

Hole doping

Tem

pera

ture

0 p0.05 0.16 0.27

TN

p*

Superconductivitydevelopps

on full Fermi surface

Tc

Superconductivitydevelopps

Partially on the Fermi surface

Normal state and Pseudo-gap


TC


AFMott

insulator

Hole doping

Tem

pera

ture

0 p0.05 0.16 0.27

TN

PseudoGap

T*

« strange Metal »ρ∝T

Normal Metalρ∝T2

p*

0 200 400 600 800 1000

Hg-1201R

aman

suc

eptib

ility

χ"(ω

) (u.

a.)

Raman shift (cm-1)

12K

Raman observation of the Pseudo-Gap

B1g anti-nodes

close to optimal

Tc = 95 K

A. Sacuto et al. Rep. of French Science Academy 2011

Pair breakingpeak

110K

150K

Pseudogap

Lost ofpair breaking peak

Comparison between the Raman PG and others technics

W.Guyard et al. not yet published, 09 T. Kondo et al. Nature 457, 09

-1000 -500 0 500 10000

10

20

Ram

an s

ucep

tibili

ty χ

"(ω

) (u.

a.)

Hg-1201

p = 0.16 UD 95 K

B1g A-Nodal

Symmetrized Raman shift (cm-1)

S N RT Bi-2201

Tc=29K

Energy (meV)0 20 40

ARPESERS

Analogy between Raman responsefunction and optical conductivity

Shastry-Shraiman relation (PRL 65, 1997)(from Kubo formula)

X Ω

τ Life timeof qsp

Raman PG and c- axis optical conductivity

The out-of-plane hopping which is modulated by the in-plane momentum in such a way that itis strongly governed by qps located along the BZ axes t⊥ (k) = t⊥0 [cos(kx) − cos(ky)]

0 200 400 600 800 1000

0.01

0.02

0.03

Ram

an in

tens

ity a

rb.u

nits

Raman shift Ω cm-1

B1g coskx-cosky

90 K110 K130 K150 K

295

CC Homes 95

J. Phys. Chem. Sol 56, 1573, 95, O.K.Andersen

150

110

10

70

C axis

W. Guyard et al.

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