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. In this talk I will
introduce a system in which a key dynamical parameter adjusts itself in
response to the changing external conditions so that the ground state naturally
favors 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.