  Iron-based compounds (IBS) display a surprising variety of superconducting
properties that seems to arise from the strong sensitivity of these systems to
tiny details of the lattice structure. In this respect, systems that become
superconducting under pressure, like CaFe$_2$As$_2$, are of particular
interest. Here we report on the first directional point-contact
Andreev-reflection spectroscopy (PCARS) measurements on CaFe$_2$As$_2$ crystals
under quasi-hydrostatic pressure, and on the interpretation of the results
using a 3D model for Andreev reflection combined with ab-initio calculations of
the Fermi surface (within the density functional theory) and of the order
parameter symmetry (within a random-phase-approximation approach in a
ten-orbital model). The almost perfect agreement between PCARS results at
different pressures and theoretical predictions highlights the intimate
connection between the changes in the lattice structure, a topological
transition in the hole-like Fermi surface sheet, and the emergence on the same
sheet of an order parameter with a horizontal node line.
