Quantum Hall to charge-density-wave phase transitions in ABC-trilayer graphene

ABC-stacked trilayer graphene’s chiral band structure results in three ($n=0,1,2$) Landau level orbitals with zero kinetic energy. This unique feature has important consequences on the interaction driven states of the 12-fold degenerate (including spin and valley) N=0 Landau level. In particular, at many filling factors ${\nu }_T=\pm 5,\pm 4,\pm 2,\pm 1$ a quantum phase transition from a quantum Hall liquid state to a triangular charge density wave occurs as a function of the single-particle induced LL orbital splitting ${\mathrm{\Delta }}_{LL}$. This phase transition should be characterized by a re-entrant integer quantum Hall effect with the Hall conductivity corresponding to the {\it adjacent} interaction driven integer quantum Hall plateau.