Recently, many novel and exotic phases have been proposed by considering the role of topology in non-Hermitian systems, and their emergent properties are of wide current interest. In this work we propose the non-Hermitian generalization of semi-Dirac semimetals, which feature a linear dispersion along one momentum direction and a quadratic one along the other. We study the topological phase transitions in such two-dimensional semi-Dirac semimetals in the presence of a particle gain-and-loss term. We show that such a non-Hermitian term creates exceptional points (EPs) originating out of each semi-Dirac point. We map out the topological phase diagram of our model, using winding number and vorticity as topological invariants of the system. By means of numerical and analytical calculations, we examine the nature of edge states for different types of semi-Dirac models and establish bulk-boundary correspondence and absence of the non-Hermitian skin effect, in one class. On the other hand, for other classes of semi-Dirac models with asymmetric hopping, we restore the non-Hermitian skin effect, an anomalous feature usually present in non-Hermitian topological systems.
Keywords: non-Hermitian systems; semi-Dirac semimetals; topological phases; topological semimetals.
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