The search for topological superconductors has recently become a key issue in condensed matter physics, because of their possible relevance to provide a platform for Majorana bound states, non-Abelian statistics, and quantum computing. Here we propose a new scheme which links as directly as possible the experimental search to a material-based microscopic theory for topological superconductivity. For this, the analysis of scanning tunnelling microscopy, which typically uses a phenomenological ansatz for the superconductor gap functions, is elevated to a theory, where a multi-orbital functional renormalization group analysis allows for an unbiased microscopic determination of the material-dependent pairing potentials. The combined approach is highlighted for paradigmatic hexagonal systems, such as doped graphene and water-intercalated sodium cobaltates, where lattice symmetry and electronic correlations yield a propensity for a chiral singlet topological superconductor. We demonstrate that our microscopic material-oriented procedure is necessary to uniquely resolve a topological superconductor state.

We study a singlet-triplet Josephson junction between a conventional s-wave superconductor and an unconventional p$_{\rm x}$-wave superconductor. The Andreev spectrum of the junction yields a spontaneous magnetization in equilibrium. This allows manipulating the occupation of the Andreev levels using an ac Zeeman field. The induced Rabi oscillations manifest themselves as a resonance in the current-phase relation. For a circularly polarized magnetic field, we find a spin selection rule, yielding Rabi oscillations only in a certain interval of the superconducting phase difference.Comment: 13 pages, 6 figure