Commensurate moir\'e superlattices in anisotropically strained twisted bilayer graphene

We investigate how anisotropic strain reorganizes commensurate moir\'e superlattices and electronic structure in twisted bilayer graphene across a finite range of twist angles. Motivated by experiments demonstrating robust magic angle phenomenology under angular disorder and heterostrain, we construct exact commensurate moir\'e supercells generated by general anisotropic strain applied to the top graphene layer. At fixed effective moir\'e deformation, with particular focus on the $\pm 6.008^\circ$ twist angle, we uncover two distinct and symmetry inequivalent commensurate geometries: tilted two dimensional moir\'e superlattices and quasi one dimensional stripe like patterns. Anisotropic strain qualitatively reshapes the low energy band structure by reducing the number of Dirac points in the moir\'e Brillouin zone, leading to sharply different electronic and magnetic field responses in these regimes. Strikingly, tilted two dimensional structures near pristine angles preserve bandwidths and AA region localization comparable to the unstrained case, providing a natural explanation for the persistence of magic angle physics over a finite distortion window, whereas quasi one dimensional moir\'e patterns exhibit dimensional reduction and immediate Hofstadter butterfly splitting at infinitesimal magnetic fields. Our results identify anisotropic strain as a unifying geometric mechanism controlling commensurate moir\'e physics beyond the pristine twist angle limit.