  An important challenge in condensed matter physics is understanding
iron-based superconductors. Among these systems, the iron selenides hold the
record for highest superconducting transition temperature and pose especially
striking puzzles regarding the nature of superconductivity. The pairing state
of the alkaline iron selenides appears to be of $d$-wave type based on the
observation of a resonance mode in neutron scattering, while it seems to be of
$s$-wave type from the nodeless gaps observed everywhere on the Fermi surface
(FS). Here we propose an orbital-selective pairing state, dubbed $s \tau_{3}$,
as a natural explanation of these disparate properties. The pairing function,
containing a matrix $\tau_{3}$ in the basis of $3d$-electron orbitals, does not
commute with the kinetic part of the Hamiltonian. This dictates the existence
of both intraband and interband pairing terms in the band basis. A spin
resonance arises from a $d$-wave-type sign change in the intraband pairing
component whereas the quasiparticle excitation is fully gapped on the FS due to
an $s$-wave-like form factor associated with the addition in quadrature of the
intraband and interband pairing terms. We demonstrate that this pairing state
is energetically favored when the electron correlation effects are orbitally
selective. More generally, our results illustrate how the multiband nature of
correlated electrons affords unusual types of superconducting states, thereby
shedding new light not only on the iron-based materials but also on a broad
range of other unconventional superconductors such as heavy fermion and organic
systems.
