Designing one-dimensional well-isolated flat bands in untwisted bilayer black phosphorus by asymmetric uniaxial strain

One-dimensional (1D) flat bands in low-dimensional materials enable the study of exotic correlated phases like bond density waves, Luttinger liquids, and Mott insulators. However, the underlying mechanisms driving their formation remain elusive, and achieving well-isolated 1D flat bands in readily achievable systems remains a significant challenge. Here we present a versatile method for engineering tunable 1D flat bands in untwisted bilayer black phosphorus using asymmetric uniaxial strain to achieve differential strain in each layer. Our first-principles calculations reveal that both the highly anisotropic stacking pattern effect and the anisotropic intralayer orbital hybridization between moiré impurities (i.e., local stacking configurations) play critical roles in the formation of 1D flat bands. Notably, asymmetric armchair strain can generate 1D well-isolated flat bands at experimentally accessible strains owing to its pronounced stacking pattern effect. This configuration provides an opportunity to directly observe 1D flat band dispersion using angle-resolved photoemission spectroscopy. Furthermore, we demonstrate that transitioning from 1D to 2D flat bands is possible by applying asymmetric biaxial strain. Our work establishes asymmetric strain as a powerful tool for engineering flat bands in bilayer systems and opens new avenues for exploring 1D strongly correlated electron systems.