Point-gap topological phases of non-Hermitian systems exhibit exotic boundary states that have no counterparts in Hermitian systems. Here, we develop a classification of second-order point-gap topological phases protected by reflection symmetry. Based on this classification, we propose exceptional second-order topological insulators, exhibiting second-order boundary states stabilized by point-gap topology. As an illustrative example, we uncover a two-dimensional exceptional second-order topological insulator with point-gapless corner states. Furthermore, we identify a three-dimensional exceptional second-order topological insulator that features hinge states with isolated exceptional points, representing second-order topological phases intrinsic to non-Hermitian systems. In this work, we enlarge the family of point-gap topological phases in non-Hermitian systems.

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• Topological phases of matter
• Non-Hermitian systems
• Topological materials
• Tight-binding model