Review of typical behaviours observed in strongly correlated - - PowerPoint PPT Presentation

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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 Some examples

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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 4 2

  • 2
  • 4

25 20 15 10 5

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
  • scillations 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).

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From 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
  • f interactions by excitations electron-hole
  • Oxides

Effective t can be small U/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 effect

Magnetic impurities

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DMFT

  • Dynamical mean field theory
  • To put together quasiparticules and

Hubbard states

  • Limit: no Q dependence, cluster DMFT…
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From 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

superconducting materials

Two different scales

  • f 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

1 2 3 4 2 4 6 8 10 10-

2

10

1

10

4

10

7

10

1

30K M (μB/f.u.) R (Ω) B (T)

?

ISOLANT METAL

1 2 3 4 2 4 6 8 10 10-

2

10

1

10

4

10

7

10

1

30K M (μB/f.u.) R (Ω) B (T)

?

ISOLANT METAL

Electronic phase separation Jahn Teller effect = orbital ordering Colossal magnetoresistance

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From R. Sopracase From C. Martin

10

  • 3

10

  • 2

10

  • 1

10 10

2

10

4

30K 4T 2T Q

  • 2

Q

  • 4

Intensity (cm

  • 1)

Q (Å)

2 3 4 5 6 7 0.0 0.2 0.4 0.6 Magnetic field (T) S/V (μm

  • 1)

Anano (a.u.) HI-M HS 2 3 4 5 6 7 0.0 0.2 0.4 0.6 Magnetic field (T) S/V (μm

  • 1)

Anano (a.u.) HI-M HS

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