A Unified Description of Dirac-Cone Anisotropies in Two Dimensions
Anisotropies in two-dimensional materials are responsible for a variety of effects that significantly modify their physical properties. In this paper, we present a covariant modification of the Dirac equation that incorporates anisotropies into the effective low-energy description around the Dirac point. The model is constructed by analogy with a Lorentz-violating extension of the Standard Model of elementary particles and yields a (2+1)-dimensional framework describing physical effects such as shifted, tilted, and distorted Dirac cones through its free parameters. The proposed model thus provides a general and unified framework in which distinct anisotropy-induced modifications of the Dirac spectrum and their combinations can be systematically characterized. We further apply the model to strained graphene and show that its effective parameters can be quantitatively extracted from first-principles electronic band structures while retaining a direct geometrical interpretation. These results establish a connection between the microscopic electronic structure and a material-independent effective description of anisotropic two-dimensional Dirac systems.