  A second-order topological insulator (SOTI) in $d$ spatial dimensions
features topologically protected gapless states at its $(d-2)$-dimensional
boundary at the intersection of two crystal faces, but is gapped otherwise. As
a novel topological state, it has been attracting great interest, but it
remains a challenge to identify a realistic SOTI material in two dimensions
(2D). Here, based on combined first-principles calculations and theoretical
analysis, we reveal the already experimentally synthesized 2D material
graphdiyne as the first realistic example of a 2D SOTI, with topologically
protected 0D corner states. The role of crystalline symmetry, the robustness
against symmetry-breaking, and the possible experimental characterization are
discussed. Our results uncover a hidden topological character of graphdiyne and
promote it as a concrete material platform for exploring the intriguing physics
of higher-order topological phases.
