Josephson Scanning Tunneling Spectroscopy in d_{x^{2}-y^{2}}-Wave Superconductors: A Probe for the Nature of the Pseudogap in the Cuprate Superconductors.

Recent advances in the development of Josephson scanning tunneling spectroscopy (JSTS) have opened a new path for the exploration of unconventional superconductors. We demonstrate that the critical current I_{c}, measured via JSTS, images the spatial form of the superconducting order parameter in d_{x^{2}-y^{2}}-wave superconductors around defects and in the Fulde-Ferrell-Larkin-Ovchinnikov state. Moreover, we show that I_{c} probes the existence of phase-incoherent superconducting correlations in the pseudogap region of the cuprate superconductors, thus providing unprecedented insight into its elusive nature. These results provide the missing theoretical link between the experimentally measured I_{c} and the spatial structure of the superconducting order parameter.