The discovery of new forms of QHE in graphene and bi-layer graphene had a tremendous impact on the scientific community and demonstrated the very special electronic properties of such perfect two-dimensional systems. Probably, the most significant hallmarks of QHE result from the presence of a zero-energy Landau level which is independent of the magnetic field, and both shared by electron and hole quantum states. Single-layer graphene, bi-layer graphene and trilayer graphene have 4-fold, 8-fold and 12-fold degenerate zero-energy landau level respectively, resulting in different sequences of quantum Hall plateaus. Integer Quantum Hall effect in graphene (black), bilayer graphene (blue) and ABC trilayer graphene (red) up to magnetic field of 60T
Although mono and bi-layer graphene have been deeply studied in the past years, trilayer graphene, on the other hand, remains largely unexplored at the present time despite its tremendous interest for possible applications in nano-electronics engineering (band gap opening). The most natural explanation of this situation lies in the fact that SiO2 trilayer graphene systems usually display poor electronic mobility (less than 1000 cm2/V.s) and therefore the LL structure cannot be deeply studied in “usual” magnetic field of up to 18T. An efficient route to explore the electronic properties of trilayer graphene would focus on improvement in device’s fabrication to increase its mobility. This issue has already been successfully established. However, an alternative route is possible, e.g. studying the LL bandstructure of low mobility trilayer graphenes under very high magnetic field. Bandstructure of ABC and ABA trilayer graphene. The comparison of subsequent theoretical IQHE with experimental data allow the stacking order determination (ABC for this sample)
For the first time, we report on typical features of a fourth type of IQHE in trilayer graphene. Self-consistent Hartree calculations of Landau levels (based on the Slonczewski-Weiss-McClure tight binding model) are favorably compared to the experimental data, allowing an unambiguous determination of the stacking order between layers of graphene, which turns out to be given by the ABC stacking geometry.
Members of the laboratory involved in this activity :
Walter Escoffier ; M. Goiran ; B. Raquet ; F. Iacovella
Former members of the laboratory involved in this activity :
Amit Kumar ; Jean-Marie poumirol
Clément Faugeras, LNCMI, Grenoble, France
D. P. Arovas & M. M. Fogler, University of California, San Diego, USA
F. Guinea, ICMM, Madrid, Spain
S. Roche, CI2N & ICREA, Barcelona, Spain
Selected publications :
A. Kumar et. al. arXiv:1104.1020 (2011) - to appear in Phys. Rev. Lett.