Band flattening in slightly twisted bilayers of Bravais networks

Discovery of superconductivity in twisted bilayer graphene ignited the current intensive studies on stacked 2D materials with moire patterns, especially focusing on flat bands and associated correlated physics. Here, we demonstrate band flattening in twisted bilayers of generic but high symmetric 2D lattices, i.e., 2D Bravais networks [1]. We first show how symmetry of each network gives constraints on the effective potential governing low-energy physics in twisted bilayers. We further numerically demonstrate the band flattening due to the constrained potential using tight-binding models. From the generic theory, we can find an interesting possibility of anisotropic band flattening, in which quasi 1D band dispersion is generated from relatively isotropic original band dispersion. Rich physics is expected with the anisotropic band flattening, ranging from the valley dependent transport to the spin-orbital intertwined model in the strongly correlated limit.

[1] T. Kariyado and A. Vishwanath, arXiv:1905.02206, to appear in Phys. Rev. Research.