The carrier mobility of anisotropic two-dimensional semiconductors under longitudinal acoustic phonon scattering was theoretically studied using deformation potential theory. Based on the Boltzmann equation with the relaxation time approximation, an analytic formula of intrinsic anisotropic mobility was derived, showing that the influence of effective mass on mobility anisotropy is larger than those of deformation potential constant or elastic modulus. Parameters were collected for various anisotropic two-dimensional materials (black phosphorus, Hittorf's phosphorus, ${\mathrm{BC}}_2\mathrm{N}$, MXene, ${\mathrm{TiS}}_3$, and ${\mathrm{GeCH}}_3$) to calculate their mobility anisotropy. It was revealed that the anisotropic ratio is overestimated by the previously described method.

Graphdiyne (GDY) is an ordered two-dimensional (2D) carbon allotrope comprising sp- and sp²-hybridized carbon atoms with high degrees of π-conjugation, which features a natural band gap and superior electric properties. However, the synthesis of one- or few-layer GDY remains challenging because of the free rotation around alkyne-aryl single bonds and the lack of thickness control. We report the facile synthesis of an ultrathin single-crystalline GDY film on graphene through a solution-phase van der Waals epitaxial strategy. The weak admolecule-substrate interaction at the heterojunction drastically relaxes the large lattice mismatch between GDY and graphene. It allows the fast in-plane coupling of admolecules and slow out-of-plane growth toward the formation of an incommensurately stacked heterostructure, which is composed of single-layer graphene and few-layer ABC-stacked GDY, as directly observed by electron microscopy and identified from Raman fingerprints. This study provides a general route not only to the bottom-up synthesis of intriguing 2D acetylenic carbon allotropes but also to the device fabrication for the direct measurement of their intrinsic electrical, mechanical, and thermal properties.