We perform infrared magnetospectroscopy of Landau level (LL) transitions in dual-gated bilayer graphene. At 𝜈=4 when the zeroth LL (octet) is filled, two resonances are observed indicating the opening of a gap. At 𝜈=0 when the octet is half-filled, multiple resonances disperse nonmonotonically with increasing displacement field, 𝐷, perpendicular to the sheet, showing a phase transition at modest displacement fields from a canted antiferromagnet (CAFM) to the layer-polarized state, with a gap that opens linearly in 𝐷. When 𝐷=0 and 𝜈 is varied, resonances at ±𝜈 show an electron-hole asymmetry with multiple line splittings as the octet is progressively filled. The 𝜈=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 𝜈=0. Our results suggest additional physics is required to understand bilayer graphene at half-filling.

中文翻译：

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双层石墨烯最低 Landau 能级相变的红外光谱


我们对双门双层石墨烯中的朗道能级 （LL） 跃迁进行了红外磁谱分析。在 ν=4 时，当第 0 个 LL（八位字节）被填充时，观察到两个谐振，表明间隙打开。当八位字节半填充时，在 ν=0 处，多个共振随着垂直于薄片的位移场 D 的增加而非单调分散，显示出在适度位移场下从倾斜反铁磁体 （CAFM） 到层极化状态的相变，间隙在 D 中线性打开。当 D=0 和 ν 变化时，±ν 处的谐振显示电子-空穴不对称性，随着八位字节的逐渐填充，会出现多条线分裂。在双层石墨烯的四带模型中考虑多个紧密结合项时，ν=4 数据与平均场 Hartree-Fock 计算的预测结果具有良好的一致性。然而，即使通过结合调谐到 CAFM 基态的谷相互作用各向异性，在 ν=0 处也只能找到部分一致。我们的结果表明，需要额外的物理学来理解半填充的双层石墨烯。