Inelastic X-ray scattering in strongly correlated (Mott) insulators

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Inelastic X-ray scattering in strongly correlated
(Mott) insulators

• T. P. Devereaux

With J. Freericks (Georgetown). Work supported by
NSERC and PREA.
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Quantum Critical Points
Cuprates phase diagram

• one particle properties may be uncritical, two
  particle properties may not.
• EXAMPLE
• (Anderson) metal-insulator transition
• 1/t , DOS non-critical, s - falls to zero at
  MIT.

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Experimental data for the cuprates

Irwin et al, 1998.

• reduction of low-frequency spectral weight
• increase in the charge transfer peak
• isosbestic point at about 2100 cm-1.

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Common to other systems?
FeSi Kondo Insulator
SmB6 mixed valent insulator

• transfer of spectral weight from low frequencies
  to high as T reduced.
• occurrence of isosbestic point (spectrum
  independent of T).
• qualitatively similar to B1g in underdoped
  cuprates.

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Low energy features.
F. Venturini et al, 2002.
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Shows a clear break in behavior at a doping pc
0.22.
Indicates that the hot qps become incapable of
carrying current. -gt unconventional quantum
critical metal insulator transition for ppc.
Venturini et al, 2002.
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Inelastic X-ray scattering
M. Hasan et al, 2001 Ca2 Cu O2 Cl2

• non-dispersive peak 5.8 eV
• weak, dispersive peak 2.5-4 eV
• which features are associated with excitations
  across a Mott gap or band transitions?
• Why would an excitation across a Mott gap show
  dispersion?

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La2CuO4 Kim et al., 2002
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Light scattering processes
Incoming photon wi
Costs energy U (charge transfer energy).
Outgoing photon wf
For finite T, double occupancies lead to small
band of low energy electrons.
Electron hops, gains t.
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Metal-Insulator transition Falicov Kimball model
d8

• Correlation-induced gap drives the
  single-particle DOS to zero at U1.5
• Interacting DOS is independent of T in DMFT (Van
  Dongen, PRB, 1992)
• Examine Raman response through the (T0) quantum
  phase transition.

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Exact results Falicov-Kimball
Fixed Temperature
Fixed U2t
Spectral weight shifts into charge transfer peak
for increasing U or decreasing T.
Charge transfer peaks.

• Spectral weight shifts into charge transfer peak
  for increasing U.
• Low frequency spectral weight t2/U.

Charge transfer peaks.
small band of qps
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Integrated spectral weight and inverse Raman slope

• The Raman response is sharply depleted at low-T.
• The inverse Raman slope changes from nearly
  constant uncorrelated metallic behavior to a
  rising pseudogap or insulating behavior as the
  correlations increase.

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Inelastic X-ray results U4, n1

• high energy peak dispersionless charge
  transfer excitation U.
• low energy peak is strongly temperature
  dependent.

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Peak positions and widths
Low energy peak
High energy peak
Filled symbols peak positions. Open symbols
peak widths.
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Exact results for Hubbard model d8Nonresonant
B1g Raman scattering (n1,U2.1)

• Note the charge transfer peak as well as the
  Fermi liquid peak at low energy. As T goes to
  zero, the Fermi peak sharpens and moves to lower
  energy.
• There is no low energy and low-T isosbestic
  point, rather a high frequency isosbestic point
  seems to develop.

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Nonresonant B1g Raman scattering (n1,U3.5)

• A MIT occurs as a function of T. Note the
  appearance of the low-T isosbestic point.
• The low energy Raman response has rich behavior,
  with a number of low energy peaks developing at
  low-T, but the low energy weight increases as T
  decreases.

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Nonresonant B1g Raman scattering (n1,U4.2)

• Universal behavior for the insulator---the
  low-energy spectral weight is depleted as T goes
  to zero and an isosbestic point appears.
• The temperature dependence here is over a wider
  range than for the FK model due to the
  T-dependence of the interacting DOS.

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X-ray results Hubbard Model
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Summary and Conclusions

• Shown some exact solutions for Raman scattering
  across a MIT.
• Insulating state, depletion of low energy
  spectral weight into charge transfer peak
  universal behavior.
• Metallic state, development of low energy peak
  reflecting qp coherence.
• Elucidates dynamics near and through a quantum
  critical point.