Giant anisotropic band flattening in twisted $\Gamma$ valley semiconductor bilayers

Abstract

We propose a general theory of anisotropic band flattening in moir\'e systems at the $\Gamma$ valley. For a two-dimensional semiconductor with a rectangular unit cell of $C_{2z}$ or mirror symmetries, we find that a larger effective mass anisotropy $\eta=m_y/m_x$ of the valence or conduction bands in the monolayer will have a stronger tendency to be further enhanced in its twisted bilayer. This gives rise to strong anisotropic band flattening and correlated physics in one dimension effectively. We predict twisted bilayer black phosphorus (tBBP) has giant anisotropic flattened moir\'e bands ($\eta\sim10^4$) from ab initio calculations and continuum model, where the low energy physics is described by the weakly coupled array of one-dimensional wires. We further calculate the phase diagram based on the sliding Luttinger liquid by including the screened Coulomb interactions in tBBP, and find a large parameter space may host the non-Fermi liquid phase. We thus establish tBBP as a promising and experimentally accessible platform for exploring correlated physics in low dimensions.