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Search for FQHE in graphene. John Watson, Sumit Mondal , Robert Niffenegger 4/29/09. Outline. Integer Quantum Hall Effect Semiconductor Graphene Fractional Quantum Hall Effect Theoretical Expectations for FQHE in Graphene Proposed Experiments Suspended Graphene

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Search for fqhe in graphene

Search for FQHE in graphene

John Watson, SumitMondal, Robert Niffenegger



  • Integer Quantum Hall Effect

    • Semiconductor

    • Graphene

  • Fractional Quantum Hall Effect

  • Theoretical Expectations for FQHE in Graphene

  • Proposed Experiments

    • Suspended Graphene

    • Graphene on Graphite Substrate

Quantum hall effect
Quantum Hall Effect

2D Top View






Qhe in graphene
QHE in Graphene

  • Graphene

    • Degeneracy = 4 (spin & sub-lattice)

    • εN =+- vf(2ehBN)1/2

  • Semiconductor

    • Degeneracy = 2 (spin)

    • εN = hωc(N + 1/2)

½ Step

Room temperature qhe in graphene
Room Temperature QHE in Graphene

  • Large LL Energy Gap

  • High Carrier Concentration

  • Mobility ~ independent of Temperature

Fractional hall effect fqhe
Fractional Hall Effect (FQHE)

Coupled Electrons and Magnetic Flux reduce Effective Magnetic field

Theoretical expectations of fqhe in graphene
Theoretical Expectations of FQHE in Graphene

  • Electrons in single layer graphene are massless, relativistic Dirac quasiparticles

  • Electrons have 4-fold degeneracy because of the additional pseudo-spin degree of freedom [ SU(4) spin-valley symmetry]

  • when the Zeeman energy is sufficiently high the graphene FQHE problem maps into the problem of FQHE in GaAs in the zero Zeeman energy limit [ Jain et al. ]

  • A completely spin and valley polarized system can be achieved by using a high magnetic field

Su 4 symmetry
SU(4) symmetry

  • The most salient difference between the conventional 2DEG and graphene arises from its valley symmetry

  • slightly different effective interaction potentials in the n-th LL in strong B field

  • the polarised FQHE states in n=0 are expected to be the same in graphene as in the 2DEG because there is no difference in the effective interaction potential

  • the unpolarised FQHE states in n = 0 will be affected due to larger internal symmetry of graphene

  • the n = 1 LL in graphene is much more similar to the n = 0 LL in the 2DEG

  • the n = 1 FQHE states are more stable than those in n = 0, for the same B field value

    [Papic et al. Arxiv:0902.3233v1]

Effect of valley polarization
Effect of valley polarization

  • If the inter-valley splitting is large, the electrons will be valley polarized independent of the filling factor

  • small inter-valley splittings will affect which Landau level is the most stable

    (for example, in the ν = 2/3 case the valley unpolarized state is favored over the valley polarized states for both n = 0 and n = 1, Apalkov et al.)

  • Apalkov and Chakraborty concludes valley-polarized FQHE states should be observed experimentally for both n=0 and n=1, perhaps in a higher mobility system

Practical possibilities
Practical possibilities

  • Disorder plays a detrimental role

  • Cleaner sample, Higher mobility?

    Suspended Graphene

  • Graphene on graphite?

    The close lattice matching would introduce a mass term into the Dirac Hamiltonian which would lift the valley degeneracy of the zero energy Landau level

Summary of observed hall effects
Summary of observed Hall effects

  • 1Stormer, H. Nobel Lecture: The fractional quantum Hall effect. Reviews of Modern Physics71, 875 (1999).

  • 2Zhang, Y. et al. Experimental observation of the quantum Hall effect and Berry’s phase in graphene. Nature438, 201-204 (2005).

  • 3Novoselov, K.S. et al. Room temperature quantum Hall effect in graphene. Science315, 1379 (2007).



E-beam lithography


90 s buffered oxide etch



Bolotin, K.I. et al. Ultrahigh electron mobility in suspended graphene. Solid State Communications146, 351-355 (2008).

Reported results
Reported results

  • Mobility increase from 28,000 cm2/Vs to 230,000 cm2/Vs

b: AFM of device

c: AFM after O2 plasma

High mobility sample on substrate

Before annealing

After annealing

Conclusions on mobility
Conclusions on mobility

  • Mean free path ~ 1.2 μm

  • Remaining scattering due to edges and electrodes

  • Fabricate larger devices

  • Annealing works because defects present above and below graphene

Secondary approach
Secondary approach

Li, G. et al. Scanning tunneling spectroscopy of graphene on graphite. Physical Review Letters102 (accepted April 2, 2009, unpublished as of April 28, 2009).

Larger separation between top & second layer

How is this graphene
How is this graphene?

  • Linear density of states ~ Dirac point

  • LL energy En ~

Differential tunneling conductance (proportional to DOS)

Summary of graphene on graphite
Summary of graphene on graphite

  • Layer spacing, DOS, and LL indicate decoupled graphene layer

  • 1Mobilities reported up to 107 cm2/Vs

  • No work reported on FQHE

1Neugebauer, P. et al. How perfect can graphene be? arXiv 0903.1612v1 (2009).