Linear response theory for shear modulus C66 and Raman quadrupole susceptibility: evidence for nematic orbital fluctuations in Fe-based superconductors.

The emergence of the nematic order and fluctuations has been discussed as a central issue in Fe-based superconductors. To clarify the origin of the nematicity, we focus on the shear modulus C(66) and the Raman quadrupole susceptibility χ(x)(2)-y(2))(Raman). Because of the Aslamazov-Larkin vertex correction, the nematic-type orbital fluctuations are induced, and they enhance both 1/C(66) and χ(x(2)-y(2))(Raman) strongly. However, χ(x)(2)-y(2))(Raman) remains finite even at the structure transition temperature T(S), because of the absence of the band Jahn-Teller effect and the Pauli (intraband) contribution, as proved in terms of the linear response theory. The present study clarifies that the origin of the nematicity in Fe-based superconductors is the nematic orbital order and fluctuations.