  Majorana bound states have been predicted to exist in vortices of topological
superconductors (SC). A realization of the Fu-Kane model, based on a
three-dimensional topological insulator brought into proximity to an $s$-wave
SC, in iron-based SC Fe(Te,Se) has attracted strong interest after pronounced
zero-energy bias peaks were observed in several experiments. Here, we show
that, by taking into account inhomogeneities of the chemical potential or the
presence of potential impurities on the surface of Fe(Te,Se), the emergence of
these zero-energy bias peaks can be explained by trivial Andreev bound states
(ABSs) whose energies are close to zero. Our numerical simulations reveal that
the ABSs behave similarly to Majorana bound states. ABSs are localized only on
the, say, top surface and cannot be distinguished from their topological
counterparts in transport experiments performed with STM tips. Thus, such ABSs
deserve a careful investigation of their own.
