  In superconductors with unconventional pairing mechanisms, the energy gap in
the excitation spectrum often has nodes, which allow quasiparticle excitations
at low energies. In many cases, e.g. $d$-wave cuprate superconductors, the
position and topology of nodes are imposed by the symmetry, and thus the
presence of gapless excitations is protected against disorder. Here we report
on the observation of distinct changes in the gap structure of iron-pnictide
superconductors with increasing impurity scattering. By the successive
introduction of nonmagnetic point defects into BaFe$_2$(As$_{1-x}$P$_x$)$_2$
crystals via electron irradiation, we find from the low-temperature penetration
depth measurements that the nodal state changes to a nodeless state with fully
gapped excitations. Moreover, under further irradiation the gapped state
evolves into another gapless state, providing bulk evidence of unconventional
sign-changing $s$-wave superconductivity. This demonstrates that the topology
of the superconducting gap can be controlled by disorder, which is a strikingly
unique feature of iron pnictides.
