Topological phases in N -layer ABC graphene/boron nitride moiré superlattices

Rhombohedral $N = 3$ trilayer graphene on hexagonal boron nitride (TLG/BN) hosts gate-tunable, valley-contrasting, nearly flat topological bands that can trigger spontaneous quantum Hall phases under appropriate conditions of the valley and spin polarization. Recent experiments have shown signatures C 2 Chern at 1/4 hole filling, in contrast to predicted value 3. We discuss low-energy model for rhombohedral N-layer (N 1, 2, 3) aligned with (hBN) subject off-diagonal moire vector potential terms alter numbers. Our analysis suggests phase transitions be triggered by pseudomagnetic field potentials associated strain patterns, a nematic order broken rotational symmetry lead numbers are agreement recent conductivity observations.