Cuprate pseudogap: Competing order parameters or precursor superconductivity

In this paper we compare two broad classes of theories for the pseudogap in cuprate superconductors. The comparison is made in reference to measurements of the superfluid density ${\rho }_s\mathrm{}(T,x)\mathrm{}$ in ${\mathrm{YBa}}_2{\mathrm{CuO}}_{7-\delta }$ films having a wide range of stoichiometries $\delta$ or, hole doping, x. The theoretical challenge raised by these (and previous) data is to understand why the T dependence of ${\rho }_s\mathrm{}(T,x)\mathrm{}$ is insensitive to the fermionic excitation gap $\Delta \mathrm{}(T,x),$ which opens in the normal state and persists into the superconducting state, when presumably ${\rho }_s\mathrm{}\left(T\right)\mathrm{}$ is governed, at least in part, by fermionic excitations. Indeed, ${\rho }_s\mathrm{}(T,x)\mathrm{}$ seems to have a BCS-like scaling with $T_c\mathrm{}\left(x\right),$ which, although not unexpected, is not straightforward to understand in pseudogapped superconductors where $T_c\mathrm{}\left(x\right)\mathrm{}$ and the excitation gap have little in common. Here, we contrast “extrinsic” and “intrinsic” theoretical approaches to the pseudogap and argue that the former (for example, associated with a competing order parameter) exhibits more obvious departures from BCS-like T dependences in ${\rho }_s\mathrm{}\left(T\right)\mathrm{}$ than approaches, which associate the pseudogap with the superconductivity itself. Examples of the latter are the Fermi-liquid-based schemes as well as a pair fluctuation mean-field theory. Thus far, the measured behavior of the superfluid density appears to argue against an extrinsic interpretation of the pseudogap, and supports instead its intrinsic origin.