Igor Lukyanchuk Yakov Kopelevich Dirac Fermions in Graphite

GRAPHITE: 3 D semimetal HOPG or 2 D multi graphene stack ? ? ?

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

ρ(T), HOPG In best samples ρc/ ρa > 5 x 104 ρa ~ 3

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

Quantum Hall Effect, different samples (2003)

Quantum oscillations: Dirac Fermions from Phase analysis - Phys. Rev. Lett. 93, 166402 (2004)

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

Generalized formula: 2 D, 3 D, arbitrary spectrum Lifshitz-Kosevich, Shoenberg, Mineev, Lukyanchuk, Kopelevich =1/2:

Phase detection ? ? ? Experiment: Sd. Hv. A

Comparison of d. Hv. A and Sd. Hv. A Sd. H Pass-band filtering spectrum

Fan Diagram for Sd. H oscillations in Graphite Normal Dirac

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

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

QHE effect : Normal vs Dirac Normal electrons, sxy 1/H Dirac- like electrons (expected

Normal (Integer QHE) GRAPHITE: Normal vs Dirac carriers separation Rxy Dirac (Semiinteger QHE) B

Discussion: 3 D case – Fermi Surface H: point Dirac Spectrum Phase volume ~0

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

Conclusion: ► HOPG graphite = multi-graphene stack (problem: origin of carriers) Both types of

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

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

ρ(T), HOPG In best samples ρc/ ρa > 5 x 104 ρa ~ 3 μΩ cm (300 K)

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

Magneto-resistance R(H)

Quantum Hall Effect, different samples (2003)

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

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

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

Phase detection ? ? ? Experiment: Sd. Hv. A

Comparison of d. Hv. A and Sd. Hv. A Sd. H Pass-band filtering spectrum electrons holes d. Hv. A

Fan Diagram for Sd. H oscillations in Graphite Normal Dirac

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

Rxx, Kish e h

Analysis of QHE in graphite

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

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

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

Discussion: 3 D case – Fermi Surface H: point Dirac Spectrum Phase volume ~0 holes Problem: no Dirac Fermions Should be seen in experiment Normal Spectrum electrons

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

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.