  Non-Hermiticity significantly enriches the concepts of symmetry and topology
in physics. Particularly, non-Hermiticity gives rise to the ramified
symmetries, where the non-Hermitian Hamiltonian $H$ is transformed to
$H^\dagger$. For time-reversal ($T$) and sublattice symmetries, there are six
ramified symmetry classes leading to novel topological classifications with
various non-Hermitian skin effects. As artificial crystals are the main
experimental platforms for non-Hermitian physics, there exists the symmetry
barrier for realizing topological physics in the six ramified symmetry classes:
While artificial crystals are in spinless classes with $T^2=1$, nontrivial
classifications dominantly appear in spinful classes with $T^2=-1$. Here, we
present a general mechanism to cross the symmetry barrier. With an internal
parity symmetry $P$, the square of the combination $\tilde{T}=PT$ can be
modified by appropriate gauge fluxes. Using the general mechanism, we
systematically construct spinless models for all non-Hermitian spinful
topological phases in one and two dimensions, which are experimentally
realizable. Our work suggests that gauge structures may significantly enrich
non-Hermitian physics at the fundamental level.
