Nematicity from mixed S₊₋ + d_(x²-y²) states in iron-based superconductors

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.