Linear response theory around a localized impurity in the pseudogap regime of an anisotropic superconductor: precursor pairing vs the d-density-wave scenario

TL;DR

This paper derives the polarizability of electron systems in different states of high-Tc superconductors, highlighting how impurity imaging can distinguish between precursor pairing and d-density-wave order.

Contribution

It provides a detailed calculation of polarizability in superconducting, pseudogap, and dDW states, revealing distinct signatures for each, especially the nesting features in the dDW scenario.

Findings

Only the dDW state shows nesting features with wave-vector Q=(pi,pi).

The polarizability exhibits azimuthal modulation consistent with d-wave symmetry.

Hole pockets are indicated by the (q,omega) dependence of the polarizability.

Abstract

We derive the polarizability of an electron system in (i) the superconducting phase, with d-wave symmetry, (ii) the pseudogap regime, within the precursor pairing scenario, and (iii) the d-density-wave (dDW) state, characterized by a d-wave hidden order parameter, but no pairing. Such a calculation is motivated by the recent proposals that imaging the effects of an isolated impurity may distinguish between precursor pairing and dDW order in the pseudogap regime of the high-Tc superconductors. In all three cases, the wave-vector dependence of the polarizability is characterized by an azymuthal modulation, consistent with the d-wave symmetry of the underlying state. However, only the dDW result shows the fingerprints of nesting, with nesting wave-vector Q=(pi,pi), albeit imperfect, due to a nonzero value of the hopping ratio t'/t in the band dispersion relation. As a consequence of nesting, the presence of hole pockets is also exhibited by the (q,omega) dependence of the retarded polarizability.