  We show how angular momentum conservation can stabilise a symmetry-protected
quasi-topological phase of matter supporting Majorana quasi-particles as edge
modes in one-dimensional cold atom gases. We investigate a number-conserving
four-species Hubbard model in the presence of spin-orbit coupling. The latter
reduces the global spin symmetry to an angular momentum parity symmetry, which
provides an extremely robust protection mechanism that does not rely on any
coupling to additional reservoirs. The emergence of Majorana edge modes is
elucidated using field theory techniques, and corroborated by
density-matrix-renormalization-group simulations. Our results pave the way
toward the observation of Majorana edge modes with alkaline-earth-like fermions
in optical lattices, where all basic ingredients for our recipe - spin-orbit
coupling and strong inter-orbital interactions - have been experimentally
realized over the last two years.
