We analyze the dynamical response of a two-dimensional system of itinerant fermions coupled to a scalar boson φ, which undergoes a continuous transition towards nematic order with a d-wave form factor. We consider two cases: (a) when φ is a soft collective mode of fermions near a Pomeranchuk instability, and (b) when it is an independent critical degree of freedom, such as a composite spin order parameter. In both cases, the order parameter is not a conserved quantity and the d-wave fermionic polarization Π(q,Ω) remains finite even at q=0. The polarization Π(0,Ω) has similar behavior in the two cases, but the relations between Π(0,Ω) and the bosonic susceptibility χ(0,Ω) are different, leading to different forms of χ′′(0,Ω), as measured by Raman scattering. We compare our results with polarization-resolved Raman data for the Fe-based superconductors FeSe1-xSx,NaFe1-xCoxAs, and BaFe2As2.
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Acknowledgments. We thank G. Blumberg, R. Fernandes, Y. Gallais, M. Navarro-Gastiasoro, I. Paul, J. Schmalian, M. Tanatar, and V. Thorsmolle for stimulating discussions. We are thankful to G. Blumberg, W.-L. Zhang, and V. Thorsmolle for sharing unpublished data with us. This work was supported by the Office of Basic Energy Sciences, U.S. Department of Energy under Award No. DE-SC0014402 (A.K. and A.V.C.). S.L. and D.C. are supported by a postdoctoral fellowship from the Gordon and Betty Moore Foundation, under the EPiQS initiative, Grant No. GBMF-4303, at MIT. A.V.C. and D.C. acknowledge the hospitality of the Aspen Center for Physics, which is supported by NSF Grant No. PHY-1607611. A.K., D.C., E.B., and A.V.C. acknowledge the hospitality of KITP at UCSB, which is supported by NSF Grant No. PHY-1125915.