Disorder-driven transition to tubular phase in anisotropic two-dimensional materials

We develop a theory of anomalous elasticity in disordered two-dimensional flexible materials with orthorhombic crystal symmetry. Similar to the clean case, we predict the existence of infinitely many flat phases with anisotropic bending rigidity and Young's modulus showing power-law scaling with momentum controlled by a single universal exponent the very same as in the clean isotropic case. With an increase of temperature or disorder, these flat phases undergo a crumpling transition. Remarkably, in contrast to the isotropic materials where crumpling occurs in all spatial directions simultaneously, the anisotropic materials crumple into a tubular phase. In distinction to the clean case in which the crumpling transition happens at unphysically high temperatures, a disorder-induced tubular crumpled phase can exist even at room-temperature conditions. Our results are applied to anisotropic atomic single layers doped by adatoms or disordered by heavy ions bombarding.