T. Senthil- Are the cuprates doped spin liquid Mott insulators?
Inelastic X-ray scattering in strongly correlated (Mott) insulators
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Transcript of Inelastic X-ray scattering in strongly correlated (Mott) insulators
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Inelastic X-ray scattering in strongly correlated (Mott)
insulatorsT. P. Devereaux
With J. Freericks (Georgetown).
Work supported by NSERC and PREA.
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Quantum Critical PointsQuantum Critical Points
-one particle properties may be uncritical, two particle properties may not.
EXAMPLE:EXAMPLE:
(Anderson) metal-insulator transition
1/ , DOS – non-critical, - falls to zero at MIT.
Cuprates phase diagram
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Experimental data for the cuprates
• reduction of low-frequency spectral weight• increase in the charge transfer peak• isosbestic point at about 2100 cm-1.
Irwin et al, 1998.
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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.
-> unconventional quantum critical metal – insulator transition for p=pc.
Venturini et al, 2002.
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Inelastic X-ray scatteringM. 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 processesIncoming photon wi Costs energy U
(charge transfer energy).
Electron hops, gains t.
Outgoing photon wf
For finite T, double occupancies lead to small band of low energy electrons.
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Metal-Insulator transition Falicov Kimball model d=∞
• Correlation-induced gap drives the single-particle DOS to zero at U=1.5
• Interacting DOS is independent of T in DMFT (Van Dongen, PRB, 1992)
• Examine Raman response through the (T=0) quantum phase transition.
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• Spectral weight shifts into charge transfer peak for increasing U.
• Low frequency spectral weight ~ t2/U.
Exact results: Falicov-Kimball
Charge transfer peaks.
Fixed Temperature
small band of
qps
Fixed U=2t
Charge transfer peaks.
Spectral weight
shifts into charge transfer peak for
increasing U or
decreasing T.
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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 U=4, n=1
• high energy peak – dispersionless charge transfer excitation ~ U.
• low energy peak is strongly temperature dependent.
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Peak positions and widthsLow energy peak High energy peak
Filled symbols – peak positions.
Open symbols – peak widths.
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Exact results for Hubbard model d=∞Nonresonant B1g Raman scattering
(n=1,U=2.1) • 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 (n=1,U=3.5)
• 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 (n=1,U=4.2)
• 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.