Anomalous phase transitions in class-D topological systems with nonreciprocal couplings

We investigate class-D topological systems with nonreciprocal couplings and demonstrate their ability to host anomalous phase transitions. Specifically, we precisely determine the topological phase, characterized by the Chern number and bulk polarization, using the Green's function and Wilson loop approaches. We rigorously confirm the validity of the anomalous transition lines by observing a remarkable consistency between the analytical zero-energy conditions and numerical phase transition boundaries. Meanwhile, bound states are present at the anomalous transition lines, but absent at the normal transition lines. Moreover, these bound states are localized at the system boundaries and are robust to disorders. Our work demonstrates that the anomalous transition lines in class-D Hermitian systems with nonreciprocal couplings exhibit richer physical phenomena than the normal transition lines, advancing the understanding of topological phase transitions.