  Topological phases, quite generally, are difficult to come by. They either
occur under rather extreme conditions (e.g. the quantum Hall liquids, which
require high sample purity, strong magnetic fields and low temperatures) or
demand fine tuning of system parameters, as in the majority of known
topological insulators. Many perfectly sensible topological phases, such as the
Weyl semimetals and topological superconductors, remain experimentally
undiscovered. Here we introduce a system in which a key dynamical parameter
adjusts itself in response to the changing external conditions so that the
ground state naturally favours the topological phase. The system consists of a
quantum wire formed of individual magnetic atoms placed on the surface of an
ordinary s-wave superconductor. It realizes the Kitaev paradigm of topological
superconductivity when the wavevector characterizing the emergent spin helix
dynamically self-tunes to support the topological phase.
