Quantum Hall ferromagnetic states of a graphene bilayer at $\nu=-1$

It was shown recently [1] that Coulomb interaction can lift the degeneracy of the octet of states in Landau level $N=0$ of a graphene bilayer by forming different kinds of quantum Hall ferromagnetic states. In this talk, we study the sequence of phase transitions induced by an external potential difference, $\Delta_{B}$ between the layers at filling factor $\nu=-1$. With $\Delta_{B}$, the system evolves from an interlayer coherent state at small $\Delta_{B}$, to a state with mixed interlayer and inter-orbital coherence at intermediate $\Delta_ {B}$, and then into a state with inter-orbital coherence only at larger $\Delta_{B}$. We discuss the nature of the ground state of these three phases and compute the dispersion of their collective excitations in the generalized random-phase approximation. For the inter-orbital coherent state, we develop an effective pseudospin model and explain that the finite wave- vector instability of the pseudospin mode at some critical bias $\Delta_{B}^{*}$. is due to the presence of a Dzyaloshinskii- Moriya term in the Hamiltonian. This term may drive the system into a spiral state for $\Delta_{B} > \Delta_{B}^{*}$. \newline \newline $\lbrack 1\rbrack$ Yafis Barlas, R. C\^ot\'e, K. Nomura, and A. H. MacDonald, Phys. Rev. Lett. {\bf 101},097601 (2008).