Infrared spectroscopy of phase transitions in the lowest Landau levels of bilayer graphene

We perform infrared magneto-spectroscopy of Landau level (LL) transitions in dual-gated bilayer graphene. At $\nu=4$ when the zeroth LL (octet) is filled, two resonances are observed indicating the opening of a gap. At $\nu=0$ when the octet is half-filled, multiple resonances disperse non-monotonically with increasing displacement field, $D$, perpendicular to the sheet, showing a phase transition at modest displacement fields from a canted anti-ferromagnet (CAFM) to the layer-polarized state, with a gap that opens linearly in $D$. When $D=0$ and $\nu$ is varied, resonances at $\pm\nu$ show an electron-hole asymmetry with multiple line splittings as the octet is progressively filled. The $\nu=4$ data show good agreement with predictions from a mean-field Hartree-Fock calculation when accounting for multiple tight-binding terms in a four-band model of bilayer graphene. However even by incorporating a valley interaction anisotropy tuned to the CAFM ground state, only partial agreement is found at $\nu=0$. Our results suggest additional physics is required to understand bilayer graphene at half-filling.