Possible deconfined critical transition in bilayer graphene

Deconfined criticality describes a quantum transition between two ordered states with unrelated symmetry, which is not allowed in the Landau-Ginzburg-Wilson framework [1]. Although many numerical studies have shown evidence for deconfined criticality, it has not yet been observed in experiments. We point out that the conductivity measurements in suspended bilayer graphene [2] could imply the presence of such a transition. The phase transition is between two insulating phases and occurs in a finite magnetic field when we tune the electric field, both fields perpendicular to the graphene plane. We argue that in the strong coupling limit, the effective spin Hamiltonian of bilayer graphene suggests a ``N\'{e}el to a kekul\'{e} valence bond solid'' transition. We also present the study of zero-energy states in the VBS vortex near the critical point.\\[4pt] [1] T. Senthil et al, Science 303, 1490 (2004).\\[0pt] [2] R. T. Weitz et al, Science 330, 812 (2010).