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
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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
KITPC 23/07/07
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) ?
KITPC 23/07/07
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
KITPC 23/07/07
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.
KITPC 23/07/07
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)
KITPC 23/07/07
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
KITPC 23/07/07
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
KITPC 23/07/07
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
KITPC 23/07/07
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
KITPC 23/07/07
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
KITPC 23/07/07
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.