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According to topological quantum chemistry, a class of electronic materialshave been called obstructed atomic insulators (OAIs), in which a portion ofvalence electrons necessarily have their centers located on some empty$\textit{Wyckoff}$ positions without atoms occupation in the lattice. Theobstruction of centering these electrons coinciding with their host atoms isnontrivial and results in metallic boundary states when the boundary isproperly cut. Here, on basis of first-principles calculations in combinationwith topological quantum chemistry analysis, we propose two dimensionalMA$_2$Z$_4$ (M = Cr, Mo and W; A = Si and Ge, Z = N, P and As) monolayer familyare all OAIs. A typical case is the recently synthesized MoSi$_2$N$_4$.Although it is a topological trivial insulator with the occupied electronicstates being integer combination of elementary band representations, it hasvalence electrons centering empty $\textit{Wyckoff}$ positions. It exhibitsunique OAI-induced metallic edge states along the (1$\bar{1}$0) edge ofMoSi$_2$N$_4$ monolayer and the in-gap corner states at three vertices ofcertain hexagonal nanodisk samples respecting C$_3$ rotation symmetry. Thereadily synthesized MoSi$_2$N$_4$ is quite stable and has a large bulk band gapof 1.94 eV, which makes the identification of these edge and corner states mostpossible for experimental clarification.

Two-dimensional Obstructed Atomic Insulators with Fractional Corner Charge in MA$_2$Z$_4$ Family