Signatures of nematic quantum critical fluctuations in the Raman spectra of lightly doped cuprates

We consider the lightly doped cuprates Y0.97Ca0.03BaCuO6.05 and La2-xSrxCuO4 (with x = 0.02, 0.04), where the presence of a fluctuating nematic state has often been proposed as a precursor of the stripe or, more generically charge density wave phase, which sets in at higher doping. We phenomenologically assume quantum critical longitudinal and transverse nematic, and charge-ordering fluctuations, and investigate their effects in the Raman spectra. We find that the longitudinal nematic fluctuations peaked at zero transferred momentum account well for the anomalous Raman absorption observed in these systems in the B-2g channel, while the absence of such an effect in the B-1g channel may be due to the overall suppression of Raman response at low frequencies, associated with the pseudogap. While in Y0.97Ca0.03BaCuO6.05 the low-frequency line shape is fully accounted for by longitudinal nematic collective modes alone, in La2-xSrxCuO4, also charge-ordering modes with finite characteristic wave vector are needed to reproduce the shoulders observed in the Raman response. This different involvement of the nearly critical modes in the two materials suggests a different evolution of the nematic state at very low doping into the nearly charge-ordered state at higher doping.