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^{†}. 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 T[over ˜]=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 Letter suggests that gauge structures may significantly enrich non-Hermitian physics at the fundamental level.