Tunability of Landau Level Crossings and Fractional Quantum Hall Phases in Few Layer Ballistic Graphene

Bernal stacked trilayer graphene (TLG) has four low energy mirror symmetric bands. These bands are very electric field sensitive because electric field breaks the original mirror symmetry with respect to the middle layer of TLG. Electric field hybridizes the bands and consequently the Landau level (LL) spectrum in presence of magnetic field gets modified. We study the dependence of the LLs in TLG on electric field. TLG has many naturally occurring LL crossings due to its differently dispersing bands. This provides a great platform for studying electric field effect in terms of its LL crossing locations in phase space. Electric field couples only a specific set of LLs which led to the observation of mostly crossings rather than avoided crossing at the degeneracy points. However, interestingly, we see signatures of valley coupling due to short range electronic interaction at the crossing point of two opposite valleys of zeroth LL (N_M=0). These opposite valleys are brought into degeneracy by an electric field. We also observe some signatures of fractional quantum Hall effect in TLG.