Thanks to: T.P. Choy, R. G. Leigh

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Breakdown of Fermi Liquid Theory in doped Mott
Insulators Hidden Charge 2e Boson
Thanks to T.-P. Choy, R. G. Leigh (PRL, 99,
46404 (2007), PRB, 77, 14512 (2008), PRB, 77,
104524 (2008),...)
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UV
Strong Electron correlations
New degrees of freedom not made out of the
elemental excitations (charge 2e bosonic field)
emergence
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Cu-O plane
Mott insulator
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Why is Tc so high?
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Mott Problem NiO
Insulator ???????
Hampton Inn floor plan (N rooms N guests)
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Half-filled band
µ
U
e
Free electrons
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Isolate the relevant degrees of freedom (UV-IR
mixing)
AF
?T
Mott insulator
boring
deeper
deep
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Fermi liquids (Fermi surface systems)
T-linear Resistivity
breakdown of standard Fermi liquid picture
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Fermi liquids
Free system
e
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1,000,000 question?
How does this picture fail in high- T_c materials?
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L of single-particle addition states
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1
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Area/ of sites
n
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Mott gap
x0.0
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Mott insulator
U
N
N
PES
IPES
no hopping
Sawatzky
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Exact Result no hopping (
)
1 hole2 empty (electron addition) states
low-energy states per electron per spin1
but this is not all
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(Real Mott systems)
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PES
IPES
Sawatzky
is L2x important?
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What is the number of electrons that can be added
at low energy?
2( of dopants)2x
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There must be other degrees of freedom!
What are they?
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high-energy scale
charge 2e
low-energy mode
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New degrees of freedom become relevant
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standard approach
block diagonal in double occupancy
each blue fermion blocks 2 states 2x sum rule
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What is
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Hubbard Model
Integrate out U-scale physics
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Isolate new degree of freedom
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Key idea
Extend the Hilbert space Associate with U-scale
a new Fermionic oscillator
U
N(?)
D_i
e
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Impose a constraint is associated with
creation of double occupancy
Integrate over heavy field
Solve constraint
Exact low-energy theory (g_h appears)
Hubbard Model
Clean Coarse-graining on energy scale U
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charge 2e boson field (non-propagating)
Non-projective
?? is an emergent degree of freedom Not made out
of the elemental fields
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Experimental Results
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is irrelevant
1.) only
interactions are relevant
is homogeneous with no bare dynamics
2.)
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(No Transcript)
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Electron spectral function
t2/U60meV
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Graf, et al. PRL vol. 98, 67004 (2007).
Spin-charge separation?
Two bands!!
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Graf, et al. PRL vol. 98, 67004 (2007).
Origin of two bands
New bound state
?i is confined (no kinetic energy)
Pseudogap
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T-linear resistivity
New scenario
as x increases
EB
E
µ
T
EB0
unbound
EB0
x
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Prediction dielectric function
new quasi particle
usual Fermi liquid p-h continuum
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(No Transcript)
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2-magnons (PRB 75, 20403R), arXiv0705.0263
Peaks where they are not seen experimentally.
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summary
low-energy theory non-electron Quantum numbers
emerge--- SC boson-fermion model
Bosonnormal state properties of cuprates
Thanks to R. G. Leigh and Ting-Pong Choy, and
DMR-NSF