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Manifestation of nematic degrees of freedom in the Raman response function of iron pnictides

We establish a relation between the Raman response function in the $B_{1g}$ channel and the electronic contribution to the nematic susceptibility within the spin-driven approach to electron nematicity of the iron based superconductors. The spin-driven nematic phase, characterized by the broken $C_4$ symmetry, but unbroken $O(3$) spin-rotational symmetry, is generated by the presence of magnetic fluctuations associated with the striped phase. It occurs as a separate phase between $T_N$ and $T_s$ in systems where the structural and magnetic phase transitions are separated. Detecting the presence of nematic degrees of freedom in iron-based superconductors is a difficult task, since it involves measuring higher order spin correlation functions. We show that the nematic degrees of freedom manifest themselves in the experimentally measurable Raman response function. We calculate the Raman response function in tetragonal phase in the large $N$ limit by considering Aslamazov-Larkin type of diagrams that contain a series of inserted fermionic boxes that resemble the nematic coupling constant of the theory. These diagrams effectively account for collisions between spin fluctuations. By summing an infinite number of such higher order diagrams, we demonstrate that the electronic Raman response function shows a clear maximum at the structural phase transition in the $B_{1g}$ channel. Hence, the Raman response function can be used to probe nematic degrees of freedom.