Dynamic superconductivity responses in photoexcited optical conductivity and Nernst effect

High-Tc cuprate, alkali-doped C₆₀, and several other unconventional superconductors have very high transition temperatures Tc with respect to the energy scale of superconducting (SC) charges inferred from the superfluid density (SFD). The observed linear relationship between Tc and the SFD can hardly be expected in BCS superconductors while being reminiscent of Bose-Einstein condensation of preformed bosonic charges. As additional non-BCS-like behaviors, responses similar to those in the bulk SC states have been observed at temperatures well above Tc in the vortexlike Nernst effect, diamagnetic susceptibility, and transient optical conductivity in recent photoexcited pump-probe measurements. In this paper, we propose a coherent picture based on equilibrium and transient SFD to understand these unconventional behaviors in cuprates, K₃C₆₀, and organic superconductors. This picture assumes: (1) Dynamic SC responses in the Nernst and photoinduced measurements emerge at the formation of the local phase coherence (LPC) among wave functions of preformed bosonic pairs. (2) Its onset temperature TLPC is distinct from and lower than the boson formation temperature often denoted as the ``pseudogap temperature'' T*, as TLPC is determined by the many-body boson density while T* represents attractive interaction between two fermions. (3) The bulk superconducting Tc, signaling global phase coherence, is significantly reduced from TLPC, due to the competition between the SC and antiferromagnetic (AF) order. (4) The inelastic magnetic resonance mode (MRM) controls Tc in the SC-AF competition. (5) The transient optical responses can be attributed to a change of the balance between the competing SC and AF orders caused by photoexcitation. The assumptions (1) and (2) explain the relationship between Tc and the transient SFD in photoexcited studies and equilibrium SFD in Nernst effect. (3) and (4) are inferred from the linear dependence of Tc on the MRM energy. (4) and (5) are consistent with the behaviors of the 400-cm^-1 optical responses in equilibrium and photoexcited studies and temperature dependence of the intensity of this optical mode and the MRM. Unlike previous phase-fluctuation pictures which expect dynamic responses between T* and Tc, the present picture involving competing order indicates that dynamic SC responses are seen between TLPC and Tc.