Possible high thermoelectric power factor in alkali-metal-intercalated BC$_3$: anisotropic multiple valleys originating from the van Hove singularity of graphene

We theoretically investigate the electronic structure of monolayer BC$_3$ and find that monolayer BC$_3$ hosts anisotropic multiple valleys originating from the splitting of the van Hove singularity in graphene. This splitting is caused by the inequivalency between boron and carbon atoms. To make use of the favorable electronic structure, we investigate the electronic structure of alkali-metal-intercalated BC$_3$, where intercalated atoms not only introduce the electron carriers but also suppress the interlayer coupling. We find that the interlayer transfer is effectively suppressed by potassium intercalation, by which the favorable electronic structure of monolayer BC$_3$ is kept. Finally, we perform model calculation with the onsite-energy offset, and verified that the strategy, introducing the splitting to the van Hove singularity, works well in general situations.