Self-trapping of particles from singular pockets in weakly doped AFM Mott insulator

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Self-trapping of particles from singular pockets
in weakly doped AFM Mott insulator

• Alvaro ROJO-BRAVO
• LPTMS URM 8626, Université Paris-Sud, Orsay,
  France

Ecrys - August, 2008
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Experimental motivation
Weakly electronically doped cuprate materials
ARPES
Electrons first appear located near antinodal
points (0, p) and (p,0) which are marked by the
van Hoves (VH) singularity

• Electrons pockets are very neat for weak doping.
• These pockets exist even for high doping (10).

• Note For weakly hole doped systems
• Holes are localized in nodal points (?/2, ?/2)
• AFM disappears at very weak hole doping

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Experimental motivation
Weakly electronically doped cuprate materials -
optics
Optical absorption shows the onset of the
interband transition and indicates on existence
of bound excitons
The absorption peak is a signature of excited
state which appears below the nominal insulating
gap.
Gap
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Experimental motivation - excitons
Schematic band structure
ARPES shows that spectra of electrons/holes
above/below the AFM gap 2D2Vpp are congruent,
hence the e-h excitation is highly degenerate. It
possesses the Van Hove singularity even when
single electrons are perturbed and the hole is
centered elsewhere, at (p/2,p/2).
S.R. Park, (2007)
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Model
Hamiltonian
Spectrum of electrons/holes near the gap edges
?, (anti-nodal points)
?
Spectrum of exciton
Quadratic terms, From corrugation of VH
singularity
Energy functional for electron near impurity with
potential V(r)
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Model
Amplitude breathing mode ?
Interaction of the electron / exciton with
deformations ? of the order parameter
(fluctuations of ?)
Energy functional for selftrapping
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Results of simulations
Localized state of one electron trapped by a
point impurity
Self-trapped state - polaron for one electron due
to interaction with amplitude mode
Amplitude is not constant, as it would be for
free electrons
This state is a collective state, which has an
energy lower than the free electrons
Neither of these bound states would exist for
hole doped cases
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Results of simulations
The exciton
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Results of simulations

• Evolution of the self-trapped state and its
  gradual of suppression by increasing the
  corrugation of the van Hoves singularity

Weakness of quadratic terms t is crucial for
the existence of the polarons. For elevated
values of t the polaron disappears.
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Conclusions

• The VH singularity endorses the trapped and
  self-trapped states for added electrons and for
  optical excitons.
• Quadratics terms ( t) corrugated VH and weaken
  self-trapped states.
• The optical exciton is not affected by
  corrugations of VH singularity, it will be always
  strongly shifted inside the gap.