(A) A mimic triangular lattice of the Hubbard model for the AB sites and the variation of U and t due to AB site expansion. (B) Carrier transfer between the B-band and LHB/UHB. Forward scanning of V_BG results in the releasing of holes and the backward scanning of V_BG results in the filling of holes in the bands. Charge transferring between the B-band and LHB/UHB shows different behaviors near the gap region of the Hubbard bands. (C) Displacement field effects on the full filling and half filling gap positions. The full filling states are independent of the D field as indicated by the thin solid line. However, the half filling is D-dependent which deviates from the ideal positions as indicated by the right side thin solid line.