Igor Luk’yanchuk, Yakov Kopelevich

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Presentation transcript:

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)

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….

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

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

ρa(T,H)

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

Phase detection ??? SdH dHvA Experiment:

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

Fan Diagram for SdH 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)

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

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

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

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

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.