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Dirac Fermions in Graphite and Graphene: Implications to QHE

Igor Luk’yanchuk, Yakov Kopelevich. Dirac Fermions in Graphite and Graphene: Implications to QHE. - Phys. Rev. Lett. 93, 166402 (2004) - Phys. Rev. Lett. 97, 256801 (2006). GRAPHITE: 3D semimetal HOPG or 2D multi graphene stack ???. - Yes.

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Dirac Fermions in Graphite and Graphene: Implications to QHE

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  1. Igor Luk’yanchuk, Yakov Kopelevich Dirac Fermions in Graphite and Graphene: Implications to QHE - Phys. Rev. Lett. 93, 166402 (2004) - Phys. Rev. Lett. 97, 256801 (2006)

  2. GRAPHITE: 3D semimetal HOPG or 2D multi graphene stack ??? - Yes Relation between QHE, Dirac fermions, Berry phase…. In graphite and graphene….

  3. Our statement: Graphite = stack of graphene monolayers EXPERIMENTAL BACKGROUND: Y. Kopelevich 2001-2005

  4. ρ(T), HOPG In best samples ρc/ ρa > 5x104 ρa ~ 3 μΩ cm (300K)

  5. ρa(T,H)

  6. ρ (ө), different samples No coherence Peak !!!

  7. Magneto-resistance R(H)

  8. Quantum Hall Effect, different samples (2003)

  9. Quantum oscillations: Dirac Fermions from Phase analysis - Phys. Rev. Lett. 93, 166402 (2004) Rxy Rxx B (T) How to detect Dirac fermions ????

  10. Landau quantization: Normal vs Dirac Normal electrons ‘’gap’’ Dirac electrons no ‘’gap’’ !!!

  11. Generalized formula: 2D, 3D, arbitrary spectrum Lifshitz-Kosevich, Shoenberg, Mineev, Lukyanchuk, Kopelevich =1/2: normal carriers =0: Dirac fermions

  12. Experiment: SdH dHvA Phase detection ???

  13. Comparison of dHvA and SdH SdH dHvA Pass-band filtering SdH dHvA spectrum electrons holes

  14. Fan Diagram for SdH oscillations in Graphite Normal Dirac

  15. Result: spectrum of quantum oscillations in HOPG Normal electrons Dirac holes

  16. Rxx, Kish e h

  17. Analysis of QHE in graphite

  18. QHE in graphite Rxy Rxx Y. Kopelevich et al. Phys. Rev. Lett. 90, 156402 (2003)

  19. QHE effect : Normal vs Dirac Normal electrons, sxy 1 / H Dirac- like electrons (expected for graphene) sxy 1 / H Gusynin Sharapov

  20. Normal (Integer QHE) GRAPHITE: Normal vs Dirac carriers separation Rxy Dirac (Semiinteger QHE) Rxx Filtering B (T)

  21. 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

  22. Another confirmation: Dirac+Normal fermions in HOPG TEM results: E. Andrei et al. 2007, Nature Phys.

  23. 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.

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