Zero momentum topological insulator in 2D semi-Dirac materials

Semi-Dirac materials in 2D present an anisotropic dispersion relation, linear along one direction and quadratic along the perpendicular one. This study explores the topological properties and the influence of disorder in a 2D semi-Dirac Hamiltonian. Energy-dependent edge states appear only in one direction, localized on either the upper or lower edge of the nanoribbon determined by their particle or hole character. Their topological protection can be rigorously founded on the Zak phase of the one-dimensional reduction of the semi-Dirac Hamiltonian, that depends parametrically on one of the momenta. In general, only a single value of the momentum, corresponding to a zero energy mode, is topologically protected. We explore the dependence on the disorder of the edge states and the robustness of the topological protection in these materials. We also explore the consequences of the topological protection of the zero-momentum state in the transport properties for a two-terminal configuration.