Dirac Fermions in Graphite and Graphene: Implications to QHE

- Phys. Rev. Lett. 93, 166402 (2004)- Phys. Rev. Lett. 97, 256801 (2006)

Igor Luk’yanchuk, Yakov Kopelevich

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

Relation between QHE, Dirac fermions, Berry phase….In graphite and graphene….

EXPERIMENTAL BACKGROUND:

Y. Kopelevich 2001-2005

Our statement: Graphite = stack of graphene monolayers

ρ(T), HOPG

In best samples

ρc/ ρa > 5x104

ρa ~ 3 μΩ cm (300K)

ρa(T,H)

No coherence Peak !!!

ρ (ө), different samples

Magneto-resistance R(H)

Quantum Hall Effect, different samples (2003)

Quantum oscillations: Dirac Fermions from Phase analysis

- Phys. Rev. Lett. 93, 166402 (2004)

How to detect Dirac fermions ????

Rxy

Rxx

B (T)

Normal electrons

Dirac electrons

Landau quantization: Normal vs Dirac

‘’gap’’

no ‘’gap’’ !!!

Generalized formula: 2D, 3D, arbitrary spectrum

Lifshitz-Kosevich, Shoenberg, Mineev, Lukyanchuk, Kopelevich

=1/2: normal carriers=0: Dirac fermions

Phase detection ???

SdHdHvA

Experiment:

SdH dHvA

dHvASdH

Pass-band filtering

spectrum

Comparison of dHvA and SdH

electrons

holes

Fan Diagram for SdH oscillations in Graphite

Normal

Dirac

Result: spectrum of quantum oscillations in HOPG

Normalelectrons

Dirac holes

29.3722 58.7444 88.1166 117.4888 146.8610

0.5

1

1.5

2

2.5

Rxx, Kishe

h

Analysis of QHE in graphite

QHE in graphite

Rxx

Rxy

Y. Kopelevich et al. Phys. Rev. Lett. 90, 156402 (2003)

QHE effect : Normal vs Dirac

Normal electrons,

Dirac- like electrons(expected for graphene)

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

1/H

xy

1 / H

xy

1 / H

xy

Gusynin Sharapov

GRAPHITE: Normal vs Dirac carriers separation

Filterin

g

Rxy

Rxx

B (T)

Normal (Integer QHE)

Dirac (Semiinteger QHE)

holes

electrons

Discussion:

3D case – Fermi Surface

Dirac Spectrum

Normal Spectrum

H: point

Phase volume ~0

Problem: no Dirac FermionsShould be seen in experiment

E. Andrei et al. 2007, Nature Phys.

Dirac+Normal fermions in HOPGTEM results:

Another confirmation:

► 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.

Conclusion: