Twisted bilayer BC${}_3$: Valley interlocked anisotropic flat bands

Abstract

Here we propose BC${}_3$, a graphene derivative that has been synthesized, as a platform to realize exotic quantum phases by introducing a moiré pattern with mismatched stacking. In twisted bilayer BC${}_3$, it is shown that a crossover from two-dimensional to quasi one-dimensional band structure takes place with the twist angle as a control parameter. This is a typical manifestation of the guiding principle in van der Waals stacked systems: the quantum interference between Bloch wave functions in adjacent layers has a striking effect on the effective interlayer tunneling. Interestingly, quasi one-dimensionalization happens in a valley dependent manner. Namely, there is interlocking between the valley index and the quasi-1D directionality, which makes BC${}_3$ a plausible candidate for valleytronics devices. In addition, the strongly correlated regime of the valley interlocked quasi-1D state reduces to an interesting variant of the Kugel-Khomskii model where intertwined valley and spin degrees of freedom potentially induces exotic quantum phases. Notably, this variant of the Kugel-Khomskii model cannot be realized in conventional solids due to the three fold valley degeneracy.

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• Anisotropic moiré band flattening in twisted bilayers of M-valley MXenes
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• Possible high thermoelectric power factor in alkali-metal-intercalated BC${}_3$: anisotropic multiple valleys originating from the van Hove singularity of graphene
• Dislocation Patterning as a Mechanism for Flat Band Formation