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

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

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

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, (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. Phase detection ???
SdH
dHvA
Experiment:

13. Pass-band filtering Comparison of dHvA and SdH SdH dHvA 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, (2003)

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

20. Filtering 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: exist in Graphite.
► 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.