Twisted bilayer <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mtext>BC</mml:mtext><mml:mn>3</mml:mn></mml:msub></mml:math>: Valley interlocked anisotropic flat bands
Toshikaze Kariyado
Abstract
Here we propose ${\mathrm{BC}}_{3}$, a graphene derivative that has been synthesized, as a platform to realize exotic quantum phases by introducing a moir\'e pattern with mismatched stacking. In twisted bilayer ${\mathrm{BC}}_{3}$, it is shown that a crossover from two-dimensional to quasi-one-dimensional (quasi-1D) 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 ${\mathrm{BC}}_{3}$ 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 induce exotic quantum phases. Notably, this variant of the Kugel-Khomskii model cannot be realized in conventional solids due to the threefold valley degeneracy.