We demonstrate that in iron-based superconductors, the extended S_{+-} SC
state coexists with the d_{x^2-y^2} state under generic conditions. The mixed
S_{+-} + d_{x^2-y^2} SC is a natural nematic state in which the tetragonal
symmetry C_4 is broken to C_2 explaining puzzling findings of nematic SC in
FeSe films [Science 332, 1410 (2011)]. Moreover, we report the possibility of a
first order transition at low-T from the nematic S_{+-} + d_{x^2-y^2} state to
the pure d_{x^2-y^2} state induced by the Zeeman magnetic field proposing an
original experimental strategy for identifying our mixed nematic state in FeSe
films. Extrapolating our findings, we argue that nematicity in non
superconducting states of underdoped and undoped pnictides may reflect mixed
S_{+-} + d_{x^2-y^2} Density Wave states.Comment: Improvements and corrections in the texte, references adde