Mechanism of Pseudogap Detected by Electronic Raman Scattering: Phase Fluctuation or Hidden Order?

We study the electronic Raman scattering in the cuprates to distinguish the two possible scenarios of the pseudogap normal state. In one scenario, the pseudogap is assumed to be caused by phase fluctuations of the preformed Cooper pairs. We find that pair-breaking peaks appear in both the B-1g and B-2g Raman channels, and they are smeared and tend to shift to the same energy with the increasing strength of phase fluctuations. Thus both channels reflect the same pairing energy scale, irrespectively of the doping level. In another scenario, the pseudogap is assumed to be caused by a hidden order that competes with the superconducting order. As an example, we assume that the hidden order is the d-density-wave (DDW) order. We find analytically and numerically that in the DDW normal state there is no Raman peak in the B-2g. channel in a tight-binding model up to the second nearest-neighbor hopping, while the Raman peak in the B-1g channel reflects the energy gap caused by the DDW order. This behavior is in agreement with experiments in the pseudogap normal state. To gain further insights, we also calculate the Raman spectra in the DDW+SC state. We study the doping and temperature dependence of the peak energy in both channels and find a two-gap behavior, which is in agreement with recent Raman experiments. Therefore, our results shed light on the hidden order scenario for the pseudogap.