Transcript Raman scattering in correlated metals and insulators

Inelastic X-ray scattering in
strongly correlated (Mott)
insulators
T. P. Devereaux
With J. Freericks (Georgetown).
Work supported by NSERC and PREA.
IXS Workshop, 7/22/2015
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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.
IXS Workshop, 7/22/2015
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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 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
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7/22/2015
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Mott ,gap
or band transitions?
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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
Electron hops,
gains t.
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For finite T, double
occupancies lead to
small band of low
energy electrons.
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Metal-Insulator transition
Falicov Kimball model d=∞
• Correlationinduced 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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Exact results: Falicov-Kimball
Fixed Temperature
• Spectral weight
Charge
shifts into charge
transfer
transfer peakpeaks.
for
increasing U.
• Low frequency
spectral weight ~
2/U.
t
small
band of
qps
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Fixed U=2t
Spectral
weight
shifts into
charge
transfer
peak for
increasing
U or
decreasing
T.
T. P. Devereaux
Charge
transfer
peaks.
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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 widths
Low 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 lowT, 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.
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