Dynamic superconductivity responses in photoexcited optical conductivity and Nernst effect

Abstract

High-${T}_{\mathrm{c}}$ cuprate, alkali-doped ${\mathrm{C}}_{60}$, and several other unconventional superconductors have very high transition temperatures ${T}_{\mathrm{c}}$ with respect to the energy scale of superconducting (SC) charges inferred from the superfluid density (SFD). The observed linear relationship between ${T}_{\mathrm{c}}$ 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 ${T}_{\mathrm{c}}$ 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, ${\mathrm{K}}_{3}{\mathrm{C}}_{60}$, 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 ${T}_{\mathrm{LPC}}$ is distinct from and lower than the boson formation temperature often denoted as the ``pseudogap temperature'' ${T}^{*}$, as ${T}_{\mathrm{LPC}}$ is determined by the many-body boson density while ${T}^{*}$ represents attractive interaction between two fermions. (3) The bulk superconducting ${T}_{\mathrm{c}}$, signaling global phase coherence, is significantly reduced from ${T}_{\mathrm{LPC}}$, due to the competition between the SC and antiferromagnetic (AF) order. (4) The inelastic magnetic resonance mode (MRM) controls ${T}_{\mathrm{c}}$ 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 ${T}_{\mathrm{c}}$ and the transient SFD in photoexcited studies and equilibrium SFD in Nernst effect. (3) and (4) are inferred from the linear dependence of ${T}_{\mathrm{c}}$ on the MRM energy. (4) and (5) are consistent with the behaviors of the $400\ensuremath{-}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$ 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 ${T}_{\mathrm{c}}$, the present picture involving competing order indicates that dynamic SC responses are seen between ${T}_{\mathrm{LPC}}$ and ${T}_{\mathrm{c}}$.