  In many classes of unconventional superconductors, the question of whether
the superconductivity is enhanced by the quantum-critical fluctuations on the
verge of an ordered phase remains elusive. One of the most direct ways of
addressing this issue is to investigate how the superconducting dome traces a
shift of the ordered phase. Here, we study how the phase diagram of the
iron-based superconductor BaFe$_2$(As$_{1-x}$P$_x$)$_2$ changes with disorder
via electron irradiation, which keeps the carrier concentrations intact. With
increasing disorder, we find that the magneto-structural transition is
suppressed, indicating that the critical concentration is shifted to the lower
side. Although the superconducting transition temperature $T_c$ is depressed at
high concentrations ($x\gtrsim$0.28), it shows an initial increase at lower
$x$. This implies that the superconducting dome tracks the shift of the
antiferromagnetic phase, supporting the view of the crucial role played by
quantum-critical fluctuations in enhancing superconductivity in this iron-based
high-$T_c$ family.
