Phase diagram of the $\nu = 2$ quantum Hall state in bilayer graphene
arXiv (Cornell University)(2023)
摘要
Bilayer graphene exhibits a rich phase diagram in the quantum Hall regime, arising from a multitude of internal degrees of freedom, including spin, valley, and orbital indices. The variety of fractional quantum Hall states between filling factors $1 < \nu \leq 2$ suggests, among other things, a quantum phase transition between valley-unpolarized and polarized states at a perpendicular electric field $D^{*}$. We find the behavior of $D^{*}$ with $\nu$ changes markedly as $B$ is reduced. At $\nu = 2$, $D^{*}$ may even vanish when $B$ is sufficiently small. We present a theoretical model for lattice-scale interactions which explains these observations; surprisingly, both repulsive and attractive components in the interactions are required. Within this model we analyze the nature of the $\nu = 2$ state as a function of the magnetic and electric fields, and predict that valley-coherence may emerge for $D \sim D^{*}$ in the high $B$ regime. This suggests the system supports Kekule bond-ordering, which could in principle be verified via STM measurements.
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关键词
quantum hall state,graphene,phase,bilayer
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