Tunable Quantum Hall Edge Conduction in Bilayer Graphene through Spin-Orbit Interaction

Bilayer graphene, in the presence of a one-sided spin-orbit interaction (SOI) induced by a suitably chosen substrate, is predicted to exhibit unconventional Quantum Hall states. The new states arise due to strong SOI-induced splittings of the eight zeroth Landau levels, which are strongly layer-polarized, residing fully or partially on one of the two graphene layers. In particular, an Ising SOI in the meV scale is sufficient to invert the Landau level order between the $n=0$ and $n=1$ orbital levels under moderately weak magnetic fields $B \lesssim 10$\~T. Furthermore, when the Ising field opposes the $B$ field, the order of the spin-polarized levels can also be inverted. We show that, under these conditions, three different compensated electron-hole phases, with equal concentrations of electrons and holes, can occur at $\nu = 0$ filling. The three phases have distinct edge conductivity values. One of the phases is especially interesting, since its edge conduction can be turned on and off by switching the sign of the interlayer bias.