Quantum Hall phase diagram of ABC-trilayer graphene

At low-energies, the massive Dirac electrons in ABC-stacked trilayer graphene exhibit a cubic dispersion with a Berry phase of $3 \pi$. Landau quantization of ABC-trilayer graphene leads to a quantum Hall (QH) plateau sequence $\sigma_{xy} = \pm 4(N +3/2) e^2/h$(where $N \geq 0 $ is the Landau level index). This results in a 12-fold degenerate zero-energy Landau level (LL) which supports a degenerate set of triplet ($n=0,1,2$) LL orbitals along with the spin and valley degeneracies. In this talk, I will show that interactions within the zeroth LL induce charge gaps which drive additional integer QH plateaus at intermediate filling factors $\nu$ ($-6 < \nu < 6$). The competition of remote hopping between the layers, interactions and pseudo-spin anisotropy leads to various ferromagnetically and anti-ferromagnetically pseudo-spin ordered states. Additionally, the unique LL orbital degeneracy influences the ground state at filling factors $\nu =-5,-2,1,4$. At these filling factors, a quantum phase transition from a quantum Hall liquid state to a triangular charge-density wave occurs when an electric potential difference $\Delta _{V}$ between the layers is reduced below a critical value $\Delta_{V}^{\left( c\right)}$