Les materiaux ferroelectriques: du bulk vers nanofilms

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Igor Lukyanchuk, Yakov Kopelevich
Dirac Fermions in Graphite and Graphene
Implications to QHE
- Phys. Rev. Lett. 93, 166402 (2004) - Phys. Rev.
Lett. 97, 256801 (2006)
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GRAPHITE 3D semimetal HOPG or 2D multi graphene
stack ???
- Yes
Relation between QHE, Dirac fermions, Berry
phase. In graphite and graphene.
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Our statement Graphite stack of graphene
monolayers
EXPERIMENTAL BACKGROUND Y. Kopelevich 2001-2005
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?(T), HOPG
In best samples ?c/ ?a gt 5x104 ?a 3 µO cm
(300K)
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?a(T,H)
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? (?), different samples
No coherence Peak !!!
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Magneto-resistance R(H)
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Quantum Hall Effect, different samples (2003)
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Quantum oscillations Dirac Fermions from Phase
analysis
- Phys. Rev. Lett. 93, 166402 (2004)
Rxy
Rxx
B (T)
How to detect Dirac fermions ????
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Landau quantization Normal vs Dirac
Normal electrons
gap
Dirac electrons
no gap !!!
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Generalized formula 2D, 3D, arbitrary spectrum
Lifshitz-Kosevich, Shoenberg, Mineev, Lukyanchuk,
Kopelevich
?1/2 normal carriers ?0 Dirac fermions
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Phase detection ???
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Comparison of dHvA and SdH
SdH
dHvA
Pass-band filtering
SdH
dHvA
spectrum
electrons
holes
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Fan Diagram for SdH oscillations in Graphite
Normal
Dirac
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Result spectrum of quantum oscillations in HOPG
Normal electrons
Dirac holes
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Rxx, Kish
e
h
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Analysis of QHE in graphite
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QHE in graphite
Rxy
Rxx
Y. Kopelevich et al. Phys. Rev. Lett. 90, 156402
(2003)
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QHE effect Normal vs Dirac
Normal electrons,
sxy
1 / H
Dirac- like electrons (expected for graphene)
sxy
1 / H
Gusynin Sharapov
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Normal (Integer QHE)
GRAPHITE Normal vs Dirac carriers separation
Rxy
Dirac (Semiinteger QHE)
Rxx
Filtering
B (T)
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Discussion 3D case Fermi Surface
H point
Dirac Spectrum
Phase volume 0
holes
Problem no Dirac Fermions Should be seen in
experiment
Normal Spectrum
electrons
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Another confirmation
DiracNormal fermions in HOPG TEM results
E. Andrei et al. 2007, Nature Phys.
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Conclusion
? HOPG graphite multi-graphene stack
(problem origin of carriers) ? Both types of
carriers (Normal and Dirac-like) exist in
Graphite. ? They have the same nature as
carriers recently identified in mono- and
bi-layer Graphene ?. Precursors of both types of
QHE exist in Graphite.