Transcript Raman scattering in correlated metals and insulators

Inelastic light scattering in
strongly correlated metals and
insulators
T. P. Devereaux
With J. Freericks (Georgetown) and R. Bulla (Augsburg).
Work supported by NSERC, PREA, US-CDRF
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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.
-> 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
• 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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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.
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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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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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