Post on 21-Jan-2016
Raman Scattering As a Probe of Raman Scattering As a Probe of Unconventional Electron Dynamics in Unconventional Electron Dynamics in
the Cupratesthe CupratesT. P. Devereaux
University of Waterloo
Generic Phase Diagram
• Fermi liquid or non Fermi liquid?
• Doped AF or AF correlated metal?
• Underlying quantum critical point(s) and crossovers?
Issues/Questions:
Key problem: to understand dynamics as a function of temperature and doping.
A Discussion of Probes:
ARPES:• Well documented evidence for strongly anisotropic spectral functions -> “hot” and “cold” qps.
Z.-X. Shen and J. R. Schrieffer, PRL 97.• Reveals 1-particle properties, but limited view on dynamics.
Transport:
• (optical, thermal), Cv(T), superfluid(T) dominated by transport along zone diagonals. Hot qps?
Raman:
Light scattering amplitude
B1g: (k) ~ cos(kxa)-cos(kya)
B2g: (k) ~ sin(kxa) sin(kya)
Clear, simultaneous view of hot (B1g ) and cold (B2g ) qps evolution with temperature and doping.
Review of Raman Data on the Cuprates:
Normal State:
Low frequencies:
• B2g - intensity largely independent of doping.
• B1g - loss of low frequency spectral weight with underdoping.
J. G. Naeini et al., PRB 1999
Exp. Review (cont.):
B1g: spectral weight shifts to 2-magnon energies ~ 3J.
T- dependence:General form for low frequency Raman response (independent of microscopic theory) –
kkk
kqp scattering rate.
k qp residue.
<…> average over Fermi surface.
Inverse of the Raman slope determines the T-dependence of the qp scattering rate.
Exp. Review (cont.):M. Opel et al., PRB 2000
B2g:
• (T) as T , same magnitude for all doping.
• follows DC transport behavior.
B1g:
• (T) as T , except for overdoped.
• qps increasingly gapped with underdoping.
• distinctly non Fermi liquid-like -> likely due to T-dependence of qp residue.
FeSi L. Cooper, 1995
Cold spot analysis of QP scattering rate:Amended cold spot model:
k(T) = c(T) + h [cos(kxa)-cos(kya)]2
c(T)= T2/T0, T0 ~ 40 meV
Zk(T) = Z0 exp{-Eg [cos(kxa)-cos(kya)]2/T}
Slightly Underdoped:
h = 470 cm-1, Eg = 140 cm-1
Slightly Overdoped:
h = 410 cm-1, Eg= 20 cm-1
Appreciably Overdoped:
h = 8 cm-1, Eg = 0 cm-1
Superconducting State:
Near optimal doping, relative peak positions, low frequency power-laws consistent with dx
2-y2
pairing.
TPD and A. Kampf, IJMPB 97
S. Sugai and T. Hosokawa, cond-mat/9912232
B2g: always
shows reorganization at Tc.
B1g: reorganization disappears with underdoping.
Bi 2212
Tc = 86K
Superconducting State (cont.):
B2g:
• shows reorganization for all doping.
• clear superconducting feature at all dopings at Tc.
• peak/Tc ~ 6 for all doping.
B1g:
• only shows reorganization for optimal and overdoped.
• no clear superconducting feature for underdoped.
• peak/Tc ~ 8 for optimal
doping, less for overdoped.
Should be viewed as having large error bars.
Summary (exp. data):
Distinctly different behavior of dynamics of BB1g1g and BB2g2g Raman response -> “hot”
and “cold” qps.
BB2g2g::
• relatively independent of doping.
• follows transport in normal state.
• shows superconducting gap proportional to Tc for all doping.
BB1g1g::
• strongly doping dependent.
• spectral weight transfer to higher energies for low dopings indicative of gapped response at different energy and temperature scale than B2g.
• Merges with B2g behavior for overdoped samples.
Raman Theory – what drives gapping of “hot” qps?Theory for inelastic light scattering exists for
• Antiferromagnetic insulators. (e.g., A. V. Chubukov and D. Frenkel, PRL 95)
• Antiferromagnetically correlated metals. (e.g., TPD and A. P. Kampf, PRB 99)
Theory lacking which takes one across MIT.
Model Calculation: Spinless Falicov-Kimball model
(with J. K. Freericks)
- exactly solvable model on a hypercubic lattice in infinite dimensions using dynamical mean field theory.
- possesses homogeneous, commensurate/incommensurate CDW phases, phase segregation, and MIT transitions.
- Raman response can be constructed formally exactly.
Light Scattering Processes:
Incoming photon i
Costs energy U (charge transfer energy).
Electron hops, gains t.
Outgoing photon f
For finite T, double occupancies lead to small band of low energy electrons.
Raman results at ½ Filling: through MIT
Weakly interacting
Pseudogap phase
insulating
MIT
Homogeneous phase
1- particle DOS is T-independent, shows MIT.
• Spectral weight shifts into charge transfer peak for increasing U.
• Low frequency spectral weight ~ t2/U.
Fixed Temperature
Charge transfer peaks.
small band of qps
Ram
an r
espo
nse
[arb
. uni
ts]
Raman results (cont):
• low frequency spectral weight begins to deplete at T ~ t2/U.
• weight piles up at U, charge transfer energy.
• reorganization of spectral weight in pseudo-gap and insulating cases.
• qualitatively similar to B1g Raman response in the cuprates.
Ram
an r
espo
nse
[arb
. uni
ts] U=2t
I low fr
eq. /
I hi
gh f
req.
Integrated Intensity
U=t
U=1.5t
U=2t
U=4t
Raman inverse slope:
U=2t
U=1.5t
U=t
U=0.5t
U=0.25t
0.1 1.0
Temperature [t]
Ram
an in
vers
e sl
ope
[arb
. uni
ts]
weakly interacting
insulating
pseudogap phase
Qualitatively similar to B1g in cuprates.
Conclusions and Summary:
Raman gives detailed evidence for 2 distinct types of dynamics related to hot and cold qps.
• B2g (cold)
• minor dependence on doping, follows transport in normal state.
• reveals superconducting gap which tracks Tc for all doping.
• B1g (hot)
• strongly dependent on doping, shift of spectral weight -> qps gapped in normal state (presumably precursor SDW).
• superconducting gap only appears for optimal and overdoped samples -> suggests a competition for qps.