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

Abstract

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 pseudo-gap 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.

5 pages, 5 figures, plus supplemental material

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