From helical state to chiral state in ferromagnetic bilayer graphene

•The promising way to realize topological phases via bilayer graphene is studied.•Bias voltage drivens topological phase transition from helical to chiral phases.•Topological properties of spin-filtered quantum Hall and QSH phases are explored.

We explore topological phases in biased ferromagnetic bilayer graphene, formed by bilayer graphene subjected to an external ferromagnetic exchange field, under a magnetic field. The most likely way to obtain a variety of distinct broken symmetry topological phases is proposed by means of ferromagnetic exchange field. Both spin-filtered quantum Hall and quantum spin Hall (QSH) phases are found. Edge modes in this QSH phase carry charge, spin and valley currents. When both time reversal and inversion symmetries are broken, the QSH phase remains robust against weak disorder. Moreover, topological phase transition from helical phase to chiral phase can be driven by simply tuning bias voltage or Fermi energy. A few possible experimental realizations are also discussed.