Field-induced tilted Landau levels and topological phase transitions in zigzag β -graphyne nanoribbons

Using a tight-binding approach, we systematically investigate the electronic properties of zigzag-edged β -graphyne nanoribbons subjected to mutually perpendicular magnetic and electric fields. Our results reveal the emergence of tilted Landau levels, which exhibit pronounced spatial distributions and quantized transport characteristics. By incorporating Zeeman splitting, we predict the existence of a quantum spin Hall phase in the system. Furthermore, we demonstrate that a topological phase transition can be induced by modulating either the Zeeman energy or the in-plane electric field strength. To quantify these effects, we calculate the spin and charge Hall conductivities within a four-terminal transport geometry.