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The coexistence of edge states and skin effects provides the topologicallyprotected localized states at the corners of two-dimensional systems. In thispaper, we realize such corner states in the two-dimensionalSu-Schrieffer-Heeger model with the nonreciprocal hoppings. For thecharacterization of the real line gap topology, we introduce the $\mathbb{Z}_4$Berry phase protected by generalized four-fold rotational symmetry. From thephysical picture of the adiabatic connection, we find that the value of the$\mathbb{Z}_4$ Berry predicts the position of edge states. Additionally, byusing the winding number, we characterize the point gap topology of the edgespectra. From the results of these characterizations by the first-ordertopological invariants, we find that the pair of values of the $\mathbb{Z}_4$Berry phase and the winging number yields the position of the topologicallyprotected localized states.

Hybrid Higher-Order Topological Skin Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings