  Pairing symmetry which characterizes the superconducting pairing mechanism is
normally determined by measuring the superconducting gap structure
($|\Delta_k|$). Here, we report the measurement of a strain-induced gap
modulation ($\partial|\Delta_k|$) in uniaxially strained
Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ utilizing angle-resolved photoemission
spectroscopy and $in$-$situ$ strain-tuning. We found that the uniaxial strain
drives Ba$_{0.6}$K$_{0.4}$Fe$_2$As$_2$ into a nematic superconducting state
which breaks the four-fold rotational symmetry of the superconducting pairing.
The superconducting gap increases on the $d_{yz}$ electron and hole pockets
while it decreases on the $d_{xz}$ counterparts. Such orbital selectivity
indicates that orbital-selective pairing exists intrinsically in non-nematic
iron-based superconductors. The $d_{xz}$ and $d_{yz}$ pairing channels are
balanced originally in the pristine superconducting state, but become
imbalanced under uniaxial strain. Our results highlight the important role of
intra-orbital scattering in mediating the superconducting pairing in iron-based
superconductors. It also highlights the measurement of $\partial|\Delta_k|$ as
an effective way to characterize the superconducting pairing from a
perturbation perspective.
