Fragile topological band in the checkerboard antiferromagnetic monolayer FeSe

By means of the first-principles calculations and magnetic topological quantum chemistry, we demonstrate that the low-energy physics in the checkerboard antiferromagnetic (AFM) monolayer FeSe, very close to an AFM topological insulator that hosts robust edge states, can be well captured by a double-degenerate nearly flat band with fragile topology just below the Fermi level. The Wilson loop calculations identify that such fragile topology is protected by the S-4z symmetry, which gives rise to a 2D second-order topological insulator that supports the bound state with fractional charge e/2 at the sample corner. This work provides a platform to study the intriguing properties of magnetic fragile topological electronic states. Previous observations of the edge states and bound states in checkerboard AFM monolayer FeSe can also be well understood in our work.