review of typical behaviours observed in strongly...
TRANSCRIPT
Review of typical behaviours observed in
strongly correlated systems
Charles Simon Laboratoire CRISMAT, CNRS and ENSICAEN,
F14050 Caen.
“Models in magnetism: from basics aspects to practical use”Timisoara september 2009
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Some examples of strongly correlated electrons
• Superconductivity• Magnetism• Low dimensionnality• Heavy fermions• Mott insulators
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Free electrons
x 420-2-4
25
20
15
10
5
0
EF
K
Band structure (tight binding calculations)
Temperature effects (EF =1eV = 30 000K)
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Effect of electron electron repulsion U
From T. Giamarchi
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Effect of correlations
Broadening
Not so strong
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Photoemission
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Photoemission in insulators
Hubbard satellite U
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Strongly correlated metal
Peak of quasi particules
Hubbard peak
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Transport properties
• Specific heat Cp:• Sommerfeld expansion:
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Heavy fermions
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Band mass and effective mass
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De Haas Van Alphen effect
• In presence of magnetic field, it appears oscillations periodic in 1/H related to the extremum area of the Fermi surface.
• In addition, there is a magnetic field dependence of the amplitude related to effective mass. (high mass, high field).
models in magnetism timisoara 13From JP Brison
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Resistivity in T2
From R. Fresard
The prefactor A scales with γ2
Also magnetic susceptibility is Cte
condcutivity=ne2τ/m
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Thermoelectric power S
From Behnia et al.
S= k/e π2/2 T/TF (1 + 2/3 z)
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Why oxides ?
• Metal U/t small, no correlations, screening of interactions by excitations electron-hole
• Oxides
Effective t can be smallU/t large
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Oxides are interesting
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Mott insulators V2 O3
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Mott insulators V2 O3
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Organic conductor from Limelette et al.
Transfer of the spectral weight
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Kondo effect
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Kondo effectMagnetic impurities
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DMFT
• Dynamical mean field theory• To put together quasiparticules and
Hubbard states• Limit: no Q dependence, cluster DMFT…
models in magnetism timisoara 27From A. Georges
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Cobaltates Ca3 Co4 O9
From Limelette
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Specific heat
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Nickelates RNiO3
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Cuprates
• They are high Tc superconductingmaterials
Two different scalesof energies
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Overdoped cuprate: normal Fermi liquid
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From B. Vignolle
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YBaCuO underdoped
YBa2 Cu3 O6.5 (p = 0.1)
A= 5.1 nm-2= 1.9 % of the carriers
Abnormal photoemission
Fermi arcs
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Fermi surface reconstruction: small pockets
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Other interpretation: stripes
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Cuprates
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Manganites Pr0.7 Ca0.3 MnO3
0
1
2
3
4
0 2 4 6 8 1010-2
101
104
107
1010
30K
M (μ
B/f.u
.)
R (Ω
)
B (T)
?IS
OLA
NT
METAL
0
1
2
3
4
0 2 4 6 8 1010-2
101
104
107
1010
30K
M (μ
B/f.u
.)
R (Ω
)
B (T)
?IS
OLA
NT
METAL
Electronic phase separation
Jahn Teller effect = orbital orderingColossal magnetoresistance
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From R. Sopracase
From C. Martin
10-3 10-2 10-1
100
102
10430K
4T
2TQ-2
Q-4
Inte
nsity
(cm
-1)
Q (Å)
2 3 4 5 6 70.0
0.2
0.4
0.6
Magnetic field (T)
S/V
(μm
-1) A
nano (a.u.)
HI-MHS
2 3 4 5 6 70.0
0.2
0.4
0.6
Magnetic field (T)
S/V
(μm
-1) A
nano (a.u.)
HI-MHS
From D. Saurel
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Conclusions
• Effects of correlations: Fermi surface, effective mass, …– Specific heat, conductivity, magnetic
susceptibility, photoemission and dHvA effects
• Mott transition, Kondo effects– Phase separation, transfer of spectral weight
• Effects of low dimensions