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Superconducting phases with exotic symmetries that differ from the underlying crystalline lattice are at the focus of superconductivity research. Of special interest are topological superconductors where the complex order parameter possesses a non-trivial phase winding generated by broken time-reversal symmetry. 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) had major success 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.
In this talk, I will describe how STM can in fact access this phase information by utilizing a pair of atomic impurities as beam-splitters, which generate a Young-type interference pattern in the tunneling conductance. By analyzing how the real-space interference patterns of Bogoliubov quasiparticles respond to the controlled rotation of impurity configurations, we develop superconducting order parameter tomography (SOPT), a technique that reconstructs the momentum space structure of the gap function $\Delta(\vec k)$, including its phase winding.
I will discuss how features such as radial fringes, nodal directions, and rotating beams encode information about both the phase winding and the sign-changing nodes of the superconducting order parameter. This real-space tomography provides a broadly applicable route to identifying unconventional and topological superconductivity featuring non-BCS pairing.
I will also discuss an alternative technique to identify topological superconductors: spin chirality. I will demonstrate that bands with broken time reversal symmetry host non-zero chiral three-spin correlations in their ground state. Chirality in the carrier band results in a chiral three-spin RKKY interaction between localized spins coupled to carriers by s-d Hamiltonian, an effect that can be detected by local probes such as spin-sensitive STM. In systems where detecting broken time-reversal by conventional means is challenging, such as topological superconductors, local detection of spin chirality can serve as a diagnostic of superconducting topological phases. |