Valley physics in twisted bilayer BC₃

Systems where atomically thin materials are artificially assembled attract huge attention as a platform to explore exotic phenomena. Especially, in a system with slight mismatches between adjacent layers, there arises a nanoscale moiré pattern, which is regarded as a key to manipulate electronic band structure. Then, a proposal for a new stacking design leading to novel phenomena is now highly demanded.

Here, we pick up graphene derivative BC₃ and show that it gives interesting valley dependent phenomena upon making twisted bilayer. The previous theory indicates that monolayer BC₃ is a 2D semiconductor having three valleys. Then, in the twisted bilayer BC₃, it is found that the 2D band dispersion is squeezed into quasi-1D ones in a valley dependent manner. Namely, the directionality of quasi-1D bands depends on valleys, which makes twisted bilayer BC₃ promising for valleytronics. In addition, it is shown that the valley dependent 1D nature leads to spin-spin interaction crucially depending on valleys in the strongly correlated limit. Interpreting the valley degrees of freedom as orbital degrees of freedom, the effective model in the correlated limit is an interesting variant of Kugel-Khomskii model. A unique spin-valley coupling in this limit can give rise to exotic quantum phases with the twist angle as an interesting control parameter.