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Infrared and Raman study of the charge-density-wave state in the rare-earth polychalcogenides RTe n Leonardo Degiorgi Laboratorium für Festkörperphysik ETH Zürich, Switzerland
Infrared and Raman study of the charge-density-wave state in the rare-earth
polychalcogenides RTen
Leonardo DegiorgiLaboratorium für Festkörperphysik
ETH Zürich, Switzerland
Motivation
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➠ Charge ordering in low dimensions (CDW, stripes, checkerboard)➠ Impact of charge ordering on the lattice dynamics➠ Interplay between electronic and phononic degrees of freedom➠ Role played by the electron-phonon coupling➠ Fermi surface instabilities (nesting)
DiMasi et al., Phys. Rev. B52, 14516 (1995)
RTe2
R2Te5
The Rare-Earth Tellurides RTen (n=2, 2.5 and 3)
RTe3
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Reflectivity and Optical Conductivity
10-3 10-2 10-1 100 101
101 102 103 104
0
20
40
60
80
100
Photon energy [eV]
Ref
lect
ivity
[%]
MetalInsulator
[cm-1]
Photon Energy (eV)
10-3 10-2 10-1 100 101
101 102 103 104
0
5
10
15
Photon energy [eV]
1 [x10
3 S /
cm]
MetalInsulator
[cm-1]
1(
) (
cm)-1
Photon Energy (eV)
http://www.solidphys.ethz.ch/spectro/
Sacchetti et al., Phys. Rev. B74, 125115 (2006)
Optical Reflectivity of RTe3
101 102 103 104 1050.0
0.2
0.4
0.6
0.8
1.0
Frequency (cm-1)
Ref
lect
ivit
y
La
RTe3
101 102 103 104 1050.0
0.2
0.4
0.6
0.8
1.0
Frequency (cm-1)
Ref
lect
ivit
y
LaCe
RTe3
101 102 103 104 1050.0
0.2
0.4
0.6
0.8
1.0
Frequency (cm-1)
Ref
lect
ivit
y
LaCeNd
RTe3
101 102 103 104 1050.0
0.2
0.4
0.6
0.8
1.0
Frequency (cm-1)
Ref
lect
ivit
y
LaCeNdSm
RTe3
101 102 103 104 1050.0
0.2
0.4
0.6
0.8
1.0
Frequency (cm-1)
Ref
lect
ivit
y
LaCeNdSmGd
RTe3
101 102 103 104 1050.0
0.2
0.4
0.6
0.8
1.0
Frequency (cm-1)
Ref
lect
ivit
y
LaCeNdSmGdTb
RTe3
101 102 103 104 1050.0
0.2
0.4
0.6
0.8
1.0
Frequency (cm-1)
Ref
lect
ivit
y
LaCeNdSmGdTbDy
RTe3
0 2.103 4.103 6.103 8.103 1.1040.6
0.7
0.8
0.9
1.0
Frequency (cm-1)R
efle
ctiv
ity
LaCeNdSmGdTbDy
RTe3
Sacchetti et al., Phys. Rev. B74, 125115 (2006)
Plasma Frequency and Single Particle Peak in RTe3
4.30 4.35 4.40
6.0.103
8.0.103
1.0.104
1.2.104
Lattice constant (Å)
p (cm -1 )
Dy
Tb
Gd
Sm
Nd
Ce
La
RTe3
4.30 4.35 4.40
6.0.103
8.0.103
1.0.104
1.2.104
Lattice constant (Å)
p (cm -1 )
Dy
Tb
Gd
Sm
Nd
Ce
La
RTe3
4.30 4.35 4.400
2000
4000
6000
Lattice constant (Å)
SP (cm -1 )
RTe3
LaCe
Nd
Sm
Gd
Tb
Dy
4.30 4.35 4.400
2000
4000
6000
Lattice constant (Å)
SP (cm -1 )
RTe3
LaCe
Nd
Sm
Gd
Tb
Dy
Pressure Dependence of R() in CeTe3
Sacchetti et al., Phys. Rev. Lett. 98, 026401 (2007)
CDW Gap: Applied versus Chemical Pressure
Dependence
X-ray experiment at ESRF
Raman Scattering
Ek
E2
E1
ħωħω’
E1
E2ħω’ħω
Stokes Anti-Stokes
Raman Scattering in RTe3:Chemical versus Applied Pressure
Petzelt and Dvorak, J. Phys. C9, 1571 (1976)
Order Parameter versus Integrated Intensity of the Raman Modes in RTe3
4.30 4.35 4.400.00
0.02
0.04
0.06
0.08
0.00
0.01
0.02
0.03
0.04
Lattice constant (Å)
p2 /( p2 +S
SP 2 )
n CD
W
/n NS
nCDW/nNS
RTe3Dy
Tb
Gd
Sm
Nd
Ce
La
1 ( ) ( cm
)
-1
Frequency (cm-1)
2.103 5.103 104 2.104103
104
104
CeTe3
LaTe3
104
104
104
104
104NdTe3
SmTe3
GdTe3
TbTe3
DyTe3-1
-1.2
-1
-1.3
-1.5
-1.7
-1.2
2.2
3
Conclusions and Future Outlook
1 ( ) ( cm
)
-1
Frequency (cm-1)
2.103 5.103 104 2.104103
104
104
CeTe3
LaTe3
104
104
104
104
104NdTe3
SmTe3
GdTe3
TbTe3
DyTe3-1
-1.2
-1
-1.3
-1.5
-1.7
-1.2
2.2
3
Fermi Surface Gapping
Tomonaga-Luttinger Liquid
Equivalence between Chemical and Applied Pressure
Phonon Dispersion and Kohn Anomaly
4.30 4.35 4.400.00
0.02
0.04
0.06
0.08
0.00
0.01
0.02
0.03
0.04
Lattice constant (Å)
p2 /( p2 +S
SP 2 )
n CD
W
/n NS
nCDW/nNS
RTe3Dy
Tb
Gd
Sm
Nd
Ce
La
Acknowledgements
Lavagnini Sacchetti
Theory
T. Giamarchi(University of Geneva)R. Monnier(ETH Zurich)B. Delley(PSI)
Pfuner
Experiment
A. PerucchiE. ArcangelettiL. BaldassarreM. BaldiniD. Di CastroP. PostorinoS. Lupi(University La SapienzaRome and ELETTRA Trieste)
Samples
I.R. FisherN. RuY.K. ShinJ.-H. Chu(Stanford University)
