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The issue of probing the pseudogap regime of the cuprate superconductors,specifically with regard to the existence and nature of superconducting pairingcorrelations of d-wave symmetry, is explored theoretically. It is shown that ifthe d-wave correlations believed to describe the superconducting state persistinto the pseudogap regime, but with pair-potential phase-fluctuations thatdestroy their long-range nature, then the low-energy quasiparticle statesobserved near extended impurities in the truly superconducting state shouldalso persist as resonances in the pseudogap regime. The scattering ofquasiparticles by these phase-fluctuations broadens what was (in thesuperconducting state) a sharp peak in the single-particle spectral function atlow energy, as we demonstrate within the context of a simple model. This peakand its broadening is, in principle, accessible via scanning tunnelingspectroscopy near extended impurities in the pseudogap regime. If so, suchexperiments would provide a probe of the extent to which d-wave superconductingcorrelations persist upon entering the pseudogap regime, thus providing astringent diagnostic of the phase-fluctuation scenario.Comment: 8 pages, 2 figure

Probingd-wave pairing correlations in the pseudogap regime of the cuprate superconductors via low-energy states near impurities