An example of diperiodic crystal structure with semi-Dirac electronic dispersion

In the physics of two-dimensional materials, notion semi-Dirac dispersion denotes electronic dispersion which is Dirac-like along one direction in the reciprocal space, and quadratic along the orthogonal direction. In our earlier publication (Damljanović and Gajić in J Phys Condens Matter 29:185503, 2017) we have shown that certain layer groups are particularly suitable for hosting semi-Dirac dispersion in the vicinity of some points in the Brillouin zone (BZ). In the present paper we have considered tight-binding model up to seventh nearest neighbors, on a structure belonging to layer group Dg5. According to our theory, this group should host semi-Dirac dispersion at A and B points in the BZ. The structure has four atoms per primitive cell, and it is isostructural with sublattice occupied by phosphorus atoms in the layered material SnPSe${}_3$. While the first order perturbation theory of double degenerate level gives two pairs of semi-Dirac cones and correctly reproduces dispersion in the Dirac-like direction, exact diagonalisation of four-by-four tight-binding Hamiltonian shows node lines caused by accidental degeneracy in the band structure. We discuss these degeneracies in the context of von Neumann–Wigner theorem, and conclude that although dispersion remains semi-Dirac in the exact diagonalisation method, the band structure does not necessarily form cones. In order to get full picture of behavior of bands in the vicinity of semi-Dirac points, first order perturbation theory may not be sufficient and one may need higher order corrections.