Tomographic imaging of superconducting order using particle-hole interference

Superconducting phases with exotic symmetries that differ from the underlying crystalline lattice are at the focus of superconductivity research. Yet, despite intense interest, detecting the order parameter symmetry and topology remains a major challenge. Real-space imaging near atomic impurities with scanning tunneling microscopy (STM) has been highly successful in revealing nodes of the superconducting gap, in particular in cuprate superconductors, however the order parameter phase winding has so far remained inaccessible by STM techniques. We demonstrate that STM can access this phase information by exploiting Young-type quasiparticle interference patterns generated by pairs of impurities acting as beam splitters. Superconducting order parameter tomography (SOPT), a technique proposed here, utilizes the response of real-space interference patterns of Bogoliubov quasiparticles to the controlled rotation of impurity configurations, allowing us to reconstruct the momentum space structure of the gap function [Formula: see text]. As a concrete example, we consider Strontium Ruthenate, whose superconducting order remains a subject of ongoing debate, and demonstrate how SOPT can distinguish between competing order parameter candidates. The Young's interference fringes, nodal directions, and rotating beams, detected by SOPT, encode information about both the nodes and phase winding of the superconducting order parameter. This method provides a broadly applicable route to identifying unconventional and topological superconductivity and establishes particle-hole interference as a new imaging modality for superconducting order.