The expression for σ σ AHC surf is defined mod e 2 / h because a surface property ( σ σ AHC surf ) can be determined from a bulk property ( θ θ ) up to a quantum. To see this, consider a block of a material with some initial θ θ which we wrap with a 2D quantum anomalous Hall insulator with Chern index C = 1 . As long as we do this without closing the surface gap, we are able to increase σ σ AHC surf by e 2 / h without altering the bulk, and therefore without altering the axion coupling θ θ .