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Recent advances in the development of Josephson scanning tunnelingspectroscopy (JSTS) have opened a new path for the exploration ofunconventional superconductors. We demonstrate that the critical current,$I_c$, measured via JSTS, images the spatial form of the superconducting orderparameter in $d_{x^2-y^2}$-wave superconductors around defects and in theFulde-Ferrell-Larkin-Ovchinnikov state. Moreover, we show that $I_c$ probes theexistence of phase-incoherent superconducting correlations in the pseudo-gapregion of the cuprate superconductors, thus providing unprecedented insightinto its elusive nature. These results provide the missing theoretical linkbetween the experimentally measured $I_c$, and the spatial structure of thesuperconducting order parameter.

physical review letters

Josephson Scanning Tunneling Spectroscopy in $d_{x^2-y^2}$-wave  superconductors: a probe for the nature of the pseudo-gap in the cuprate  superconductors