Making topologically trivial non-Hermitian systems nontrivial via gauge fields

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.