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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. Quantum Critical Points. Cuprates phase diagram. one particle properties may be uncritical, two particle properties may not. EXAMPLE: - PowerPoint PPT Presentation
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IXS Workshop, 04/19/23 T. P. Devereaux 1
Inelastic X-ray scattering in strongly correlated (Mott)
insulatorsT. P. Devereaux
With J. Freericks (Georgetown).
Work supported by NSERC and PREA.
IXS Workshop, 04/19/23 T. P. Devereaux 2
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
IXS Workshop, 04/19/23 T. P. Devereaux 3
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.
IXS Workshop, 04/19/23 T. P. Devereaux 4
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.
IXS Workshop, 04/19/23 T. P. Devereaux 5
Low energy features.
F. Venturini et al, 2002.
IXS Workshop, 04/19/23 T. P. Devereaux 6
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.
IXS Workshop, 04/19/23 T. P. Devereaux 7
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?
IXS Workshop, 04/19/23 T. P. Devereaux 8
La2CuO4 – Kim et al., 2002
IXS Workshop, 04/19/23 T. P. Devereaux 9
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.
IXS Workshop, 04/19/23 T. P. Devereaux 10
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.
IXS Workshop, 04/19/23 T. P. Devereaux 11
• 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.
IXS Workshop, 04/19/23 T. P. Devereaux 12
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.
IXS Workshop, 04/19/23 T. P. Devereaux 13
Inelastic X-ray results U=4, n=1
• high energy peak – dispersionless charge transfer excitation ~ U.
• low energy peak is strongly temperature dependent.
IXS Workshop, 04/19/23 T. P. Devereaux 14
Peak positions and widthsLow energy peak High energy peak
Filled symbols – peak positions.
Open symbols – peak widths.
IXS Workshop, 04/19/23 T. P. Devereaux 15
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.
IXS Workshop, 04/19/23 T. P. Devereaux 16
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.
IXS Workshop, 04/19/23 T. P. Devereaux 17
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.
IXS Workshop, 04/19/23 T. P. Devereaux 18
X-ray results Hubbard Model
IXS Workshop, 04/19/23 T. P. Devereaux 19
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.