  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 fault-tolerant
quantum computing. 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 tunneling 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
state. We demonstrate that our microscopic material-oriented procedure is
necessary to uniquely resolve a topological superconductor state.
