Multi-Domain Model of Bilayer Graphene with Broken Time Reversal Symmetry

Recent experiments suggest strange new states for bilayer graphene at zero electric and magnetic fields~[1]. We consider recent models for the ground state of bilayer graphene with interactions~[2,3]. These models predict domains with non-zero local Hall conductance but an expected overall average Hall conductance of $\sigma_{xy}=0$, and should exhibit broken time reversal symmetry. We examine theoretical models for random four-probe measurements for various domain geometries in bilayer graphene at zero electric and magnetic fields. We find non-zero Hall conductance of magnitude dependent on domain geometry and network structure. \\[4pt] [1] Weitz, R.T., Allen, M.T., Feldman, B.E., Martin, J. Yacoby, A. Science. {\bf330}, 6005 (2010). \\[0pt] [2] Nandkishore, R., Levitov, LPhys. Rev. Lett. {\bf104}, 156803 (2010) \\[0pt] [3] Zhang F., Jung J., Fiete, G.A., Niu, Q., MacDonald, A.H. arXiv:1010.4003v1 (2010)