N

Monolayer BC₃ is a three-valley 2D semiconductor, and it has been theoretically proposed that by making twisted bilayer, BC₃ leads to a valley dependent quasi-1D band structure [TK, PRB (2023)]. This valley dependence could result in interesting valleytronics applications or spin-valley intertwined quantum phases.

Here, by detailed first-principles and model calculations for making comparison between BC₃ and C₃N, which is regarded as a dual material to BC₃, we clarify the essence of the origin of the valley-dependent quasi-1D band structure. Generically speaking, quantum interference between the Bloch wave functions in the upper layer and the lower layer plays essential role in determining electronic structures of twisted bilayer systems. It turns out that band dispersions of BC₃ and C₃N are well connected by particle-hole exchange. However, their wave functions have a striking difference, resulting in very different band structures in the twisted bilayer setup. This confirms the importance of the quantum interference in moire materials, giving us a guideline to search for novel band engineering in van der Waals heterostructures.

Alongside with the above electronic structure analysis, we also show the results of the large-scale calculations for the crystalline structures of the twisted bilayer BC₃ and C₃N.