  Nematic order often breaks the tetragonal symmetry of iron-based
superconductors. It arises from regular structural transition or electronic
instability in the normal phase. Here, we report the observation of a nematic
superconducting state, by measuring the angular dependence of the in-plane and
out-of-plane magnetoresistivity of Ba0.5K0.5Fe2As2 single crystals. We find
large twofold oscillations in the vicinity of the superconducting transition,
when the direction of applied magnetic field is rotated within the basal plane.
To avoid the influences from sample geometry or current flow direction, the
sample was designed as Corbino-shape for in-plane and mesa-shape for
out-of-plane measurements. Theoretical analysis shows that the nematic
superconductivity arises from the weak mixture of the quasi-degenerate s-wave
and d-wave components of the superconducting condensate, most probably induced
by a weak anisotropy of stresses inherent to single crystals.
