Topological and valleytronic materials are promising for spintronic and quantum applications due to their unique properties. Using first principles calculations, we demonstrate that germanene (Ge)-based ferromagnetic heterostructures can exhibit multiple quantum states such as quantum anomalous Hall effect (QAHE) with Chern numbers of C=-1 or C=-2, quantum valley Hall effect (QVHE) with a valley Chern number of C$v$=2, valley-polarized quantum anomalous Hall effect (VP-QAHE) with two Chern numbers of C=-1 and C$v$=-1 as well as time-reversal symmetry broken quantum spin Hall effect (T-broken QSHE) with a spin Chern number of C$s$~1. Furthermore, we find that the transitions between different quantum states can occur by changing the magnetic orientation of ferromagnetic layers through applying a magnetic field. Our discovery provides new routes and novel material platforms with a unique combination of diverse properties that make it well suitable for applications in electronics, spintronics and valley electronics.
Categories: physics.comp-ph cond-mat.mes-hall