Extended Data Fig. 9: Evolution of the band structure at charge-neutrality with D.
From: Correlated insulator and Chern insulators in pentalayer rhombohedral-stacked graphene
a, Rxx measured at n = 0 at 2 K. b, The band structure schematic of each isospin flavor at charge-neutrality under different D values. The colored dots correspond to the states in a, including LAF (layer antiferromagnet), SM (semimetal), QAH (quantum anomalous Hall) and LP (layer polarized state). The color of each band represents the valley Chern number (black: 5/2, red: -5/2), while the band with a grey color indicates the gap-closing case. c, The layer polarization of the LP, QAH and LAF state. The layer polarization of both conduction and valence band for each isospin flavor is shown, where green and orange color corresponds to the K’ and K valley. At D = 0, the system starts with the LAF state where charges are evenly distributed in the top and bottom layer in a spin-polarized manner (point A). As D increases, the gap of spin up (down) flavor expands (shrinks) due to its layer configuration (point B). It is important to note that the gap sizes of the two valleys with the same spin may differ. Consequently, one of the two gaps closes and reopens first (point C), leading to a situation where the gap of the K valley inverts while the gap of the K’ valley remains the same, resulting in the so-called QAH state (point D). Moreover, the layer polarization becomes partially polarized at this stage. If D continues to increase, the gap of the other valley eventually closes and reopens (point E), leading to the fully layer-polarized state (point F).
