Tilt and Anisotropy of the Dirac Spectrum Caused by the Overlapping of Bloch Functions

It has been shown that the overlapping of bands belonging to equivalent representation of the symmetry group is possible in systems with Dirac points appearing at the crossing of these bands. This overlapping results in the tilt and additional anisotropy of the Dirac spectrum, as well as in the renormalization of the velocity. At the same time, overlapping does not violate the general conditions of existence of the stable band crossing point. The effective Dirac Hamiltonian in the presence of band overlapping is pseudo-Hermitian and corresponds to the effective action of a massless spinor field in the curved spacetime.