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Non-Hermiticity significantly enriches the concepts of symmetry and topologyin physics. Particularly, non-Hermiticity gives rise to the ramifiedsymmetries, where the non-Hermitian Hamiltonian $H$ is transformed to$H^\dagger$. For time-reversal ($T$) and sublattice symmetries, there are sixramified symmetry classes leading to novel topological classifications withvarious non-Hermitian skin effects. As artificial crystals are the mainexperimental platforms for non-Hermitian physics, there exists the symmetrybarrier for realizing topological physics in the six ramified symmetry classes:While artificial crystals are in spinless classes with $T^2=1$, nontrivialclassifications dominantly appear in spinful classes with $T^2=-1$. Here, wepresent a general mechanism to cross the symmetry barrier. With an internalparity symmetry $P$, the square of the combination $\tilde{T}=PT$ can bemodified by appropriate gauge fluxes. Using the general mechanism, wesystematically construct spinless models for all non-Hermitian spinfultopological phases in one and two dimensions, which are experimentallyrealizable. Our work suggests that gauge structures may significantly enrichnon-Hermitian physics at the fundamental level.

Making topologically trivial non-Hermitian systems nontrivial via gauge fields