  I consider a particle in the topologically non-trivial Su-Schrieffer-Heeger
(SSH) model interacting strongly with a mobile impurity, whose quantum dynamics
is described by a topologically trivial Hamiltonian. A particle in the SSH
model admits a topological zero-energy edge mode when a hard boundary is placed
at a given site of the chain, which may be modelled by a static impurity. By
solving the two-body problem analytically I show that, when the impurity is
mobile, the topological edge states of the Su-Schrieffer-Heeger model remain
fully robust and a flat band of bound states at zero energy is formed as long
as the continuum spectrum of the two-body problem remains gapped, without the
need for any boundaries in the system. This is guaranteed for a sufficiently
heavy impurity. As a consequence of the infinite degeneracy of the zero energy
modes, it is possible to spatially localise the particle-impurity bound states,
effectively making the impurity immobile. These effects can be readily observed
using two-dimensional photonic lattices.
