KITPC 23/07/07

Gaps and pseudogaps in n and p-type cuprates from infrared

spectroscopy.Ricardo LOBO, Andrés SANTANDER-SYRO, Alexandre ZIMMERS,

Nicole BONTEMPSLaboratoire Photons et Matière – CNRS / Physique du Solide - ESPCI -

Paris

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Paul Langevin

Irène et Frédéric Joliot-Curie

Pierre-Gilles de Gennes

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Collaborators

Chris HOMES (BNL, USA)

Jin HWANG, Tom TIMUSK Mc Master University, Hamilton, Canada

Andrew MILLIS Columbia University, NY, USA

KITPC 23/07/07

Z. Konstantinovic, Z.Z. Li, H. RaffyLaboratoire de Physique des Solides, Université Paris-Sudhole doped BiSrCaCuO (Bi-2212, Bi-2201) thin films

c-axis oriented, epitaxially grown thin films / SrTiO3

C.P. Hill, M.C. Barr, Y. Dagan, R.L. GreeneCenter for Superconductivity Research, University of Maryland

Electron doped Pr2-xCexCuO (PCCO) thin filmsc-axis oriented, epitaxially grown thin films / SrTiO3

A. Forget, D. Colson Service de Physique de l’Etat Condensé, CEA Saclay, Gif-sur-

Yvette

Hole doped HgBaCuO (Hg-1201) single crystal

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1: the normal state

Introduction: reflectivity and optical functions (optical conductivity)

1. Phase diagram of high Tc cuprates2. Spectral weight, transfer of spectral weight3. Experiment and analysis4. Normal state gaps (T>Tc) in hole- and electron-doped

cuprates5. Conclusion

KITPC 23/07/07

)()()( θieRr

)()(~)(~

Rnn

at ~ normal incidence

Ei Er = r Ei

Reflectivity

)()()()(~)()( iiknnandr

TKK*

*or fit

KITPC 23/07/07

stands for high energy contributions j

j jj

jjp

ii )()()(

i

dielectric function

= i optical conductivity

Free electrons (Drude) + excitations at j

dissipation dispersion

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CuO Plane

CuO Plane

CuO Plane

p-doped La2-xSrxCuO4 (HgBaCuO)

n-doped(Nd,Pr,Sm)2-xCexCuO4

apical oxygen

High-temperature Superconductors

Bi

Sr

Ca

Cu

O

p-doped Bi2Sr2CaCu2O8

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Cu 2+

3d91 hole per site

CuO2 plane

t

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Tem

pera

ture

(K)

0

100

200

0.0 0.1 0.20.10.2

300 Bi2Sr2CaCu2O8PrxCexCuO4+y

Doping /Cu electrons holes

PG

T*

QCP?

gap?

HgBaCuO

Tunnel Alf, Dagan

ARPES, IR(Onose, Wang)

SCSC

AF

NMR, tunnel, ARPES, Cp, RamanIR(?)

Phase diagram

QCP?

KITPC 23/07/07

History….C axis optical conductivity (.cm)

C. Homes, Physica C 254, 265 (1995)

drops below T*

Underdoped YBCO

Optimally doped YBCO

drops below Tc

700

800

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1000 2000 3000 4000 (cm-1)

J. Hwang et al, cd0607653

In plane conductivity BiSrCaCuO underdoped Tc=82K

decreases

increases

T<Tc

Just a narrowing of the QP zero frequency peak

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In plane scattering rate

1000 2000

J. Hwang et al, cd/0607653 (2006)

Bi2212

J. Hwang et al, cd/0607653 (2006)

Depletion at T*>T>Tc

cm

cm

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What’s special with the optical conductivity ?

),(),(),(

TiTT p

Re),( pT

Im),( pT

Generalized Drude

Just another set of 2 optical functions .

Does the pseudogap show up only through the depletion of ,

or is there a spectral weight loss (as seen along the c axis) ?

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kdf

i

v

kk

kQP

/

Semi-classical approximation for

If a gap opens over the full Fermi surface (FS),QP → 0 up to ~

M.Norman et al 392, 157 (1998), P. Coleman ibid P.134

Bi-2212 from ARPES

If a gap (k) opens only over a part of the FS,Only part of QP is lost

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1000 2000 3000 4000 5000 60000.0

5.0x10-4

1.0x10-3

1.5x10-3

2.0x10-3

Frequency

1()

)(/)(/ TTT2< T1

T1

dTWc

D ),(

WD increases as T decreases

mne

dT

),(f - sum rule

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1000 2000 3000 4000 5000 60000.0

5.0x10-4

1.0x10-3

1.5x10-3

2.0x10-3

Frequency

1()

T1

>T* T2<T*

Opening of a partial gap at T*

dTWc

G ),(

Decrease of the related spectral weight WG integrated up to C

as T < T*, WG(T) could make W(T) decrease

Two competingSW transfer processes

W(T)=WD(T)+WG(T)

dTWc

D ),(C

NB: in order to observe that, integrate from 0: needs proper extrapolation.

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Bi2Sr2CaCu2O8+

0 500 1000 1500 20000

2000

4000

6000T

c=70K underdoped

295K 250K 200K 150K 100K 80K 40K 10K

1() (

.cm

)

Wavenumber (cm)

CuN

dTW

eff

c

c

/

)(),(

0 5000 10000 150000.0

0.2

0.4

Nef

f / C

u (

300K

)

c (cm-1)

und ovd

Look at the change vs T / 300K

A. F. Santander-Syro et al PRB 70, 134504 (2004)

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100 150 200 250 300

0.00

0.01

0.02

underdoped Tc=70K

500 1000 3000

T (K)

Ne

ff (

T,

C)

- N

eff (

30

0K

, C) overdoped T

c=63K

-0.01

0.00

0.01

5000 10000 16000 20000

C

100 150 200 250 3000.00

0.02

0.04

0.06

T (K)

-0.04

-0.02

0.00

0.02

A. Santander et al, PRL 88, 097005 (2002) revisited

W increases C W also increasing, but: saturation ~ 150K

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280240

200160

120

280240

200160

120

Temperature (K)

Energy (eV)

0.06250.250

0.6251.25

2

Bi2Sr

2CaCu

2O

8

Overdoped Underdoped

Temperature (K)

Energy (eV) 2

1.25

0.2500.0625

0.625

Pictorial sketch Bi-2212

Pseudogap from the in-plane spectral weight?

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ARPES Bi2212

The PG is clearly seen in a (kx,ky) range around

Why is optics "blind"?

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kdf

i

v

kk

kQP

/

Belief that optics probes only the nodal (N) directions in the k space

J

AN

N

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STM atomic scale pictures vs T

K. Gomes et al, Nature 447, 569 (2007)

T>>TcT=20K

What is the optical response of such an inhomogenous state?

Vs T?

300 Å

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Preliminary results: small (~5%) systematic decrease below 150K

Note: competition with QP peak narrowing underestimates the “gap opening temperature”.

100 150 200 250 300

0.00

0.05

Temperature (K)

(W(

C,T

) -

W(

C,2

95K

)) /

W(

C,2

95K

)

1000 cm-1

3000 cm-1

36000 cm-1

Hg-1201 Tc=89K – underdoped (Tcmax=95K)

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Pseudogap in hole doped cuprates

No clear signature in Bi-2212

small but significant, loss of spectral weight in slightly underdoped Hg-1201, which we assign to the PG opening

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Electron doped PrxCexCuO thin films

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0

1

2

3

4

0 500 10000

5

10

0

5

10

15

20

0 500 10000

5

10

15

20

300K 200K 100K 25K

cm

x=0.11

Frequency (cm -1)

x=0.13

x=0.15

Frequency (cm -1)

x=0.17

Real part of the optical conductivity

QP contribution

at low energyTc=15K Tc=15K

Tc=21K

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0.0

1.0

2.0

0 2000 40000.0

1.0

2.0

0 2000 4000

x=0.15

x=0.11

T

.c

m

x=0.13

Frequency (cm-1)

x=0.17

Tc=15KTc=15K

Tc=21K

Optical conductivity

0

10

20

0

2

4

0 5000

5

10

0 500 10000

20

40

Tc=21K

300K 200K 75K 25K

x=0.15

x=0.11

T

.c

m

x=0.13 Tc=15K T

c=15K

Frequency (cm-1)

x=0.17

The energy scale over which 1 is depleted is ~twice larger

KITPC 23/07/07

0 50 100 150 200 250 300

0

5x10-2

1x10-1

( N

eff(

c,T)-

Nef

f(c,3

00K

)) /

Nef

f(c,3

00K

)

Temperature (K)

1000 2000 3000 5000 16000

C (cm-1)

Gap opening at T>TW

2 < 2000 cm-1

Spectral weight

0 50 100 150 200 250 3000

1x10-1

2x10-1

3x10-1

4x10-1

( N

eff(

c,T)-

Nef

f(c,3

00K

)) /

Nef

f(c,3

00K

)

Temperature (K)

1000 2000 3000 5000 16000

C (cm-1)

X=0.17 - Tc=15K X=0.13 - Tc=15K

A. Zimmers et al, Europhys. Lett. 70, 225 (2005)

No signature of a gap

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300

250200

150100

50

300

250200

150100

50

Temperature

(Kelvi

n)

Wavelength (m

icron)

105

3.3

21

Metallic sheet W

avelength (micron)

10

5

3.3

2

1

Temperature

(Kelvi

n)

Partially gapped sheet

x=0.16 Pr2-x

CexCuO

4 x=0.13

Pictorial sketch: QP + gap

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High energy " PG" in electron doped cuprates"

0.0 0.1 0.20

100

200

300

400

500

Concentration en Ce

T(K

)

Tc

TW NCCO Onose et al.

TW PCCO

QCP ?

A. Zimmers et al. Europhys. Lett. 70, 225 (2005)

Y. Dagan et al, PRL 92, 167001 (2004)

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H. Matsui et al., 2006 APS meeting

20022002

x = 0.13 x = 0.15x = 0.16

20062006

ARPESx = 0.04 x = 0.10

N.P. Armitage et al, PRL 81, 257001 (2002)

x = 0.17

A. Santander-Syro et al, preprint

20072007

NCCO

NCCO

SCCO

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Conclusion

Signatures for a normal state gap in the infrared optical conductivity are present in both hole doped and electron doped cuprates, however very different

- Energy scales are different.- Downturn of SW significantly larger in electron

doped than in hole doped cuprates.- Different origin: the high energy PG in electron

doped cuprates is magnetic, the nature of the PG is still a question mark in hole doped cuprates.