title: Bilayer Graphene as a Platform for Bosonic Symmetry-Protected Topological States.
abstract: Bosonic symmetry protected topological (BSPT) states, the bosonic analogue of topological insulators, have attracted enormous theoretical interest in the last few years. Although BSPT states have been classified by various approaches, there is so far no successful experimental realization of any BSPT state in two or higher dimensions. In this paper, we propose that a two-dimensional BSPT state with U(1)×U(1) symmetry can be realized in bilayer graphene in a magnetic field. Here the two U(1) symmetries represent total spin S^{z} and total charge conservation, respectively. The Coulomb interaction plays a central role in this proposal-it gaps out all the fermions at the boundary, so that only bosonic charge and spin degrees of freedom are gapless and protected at the edge. Based on the above conclusion, we propose that the bulk quantum phase transition between the BSPT and trivial phase, which can be driven by applying both magnetic and electric fields, can become a "bosonic phase transition" with interactions. That is, only bosonic modes close their gap at the transition, which is fundamentally different from all the well-known topological insulator to trivial insulator transitions that occur for free fermion systems. We discuss various experimental consequences of this proposal.
authors.affiliation: Department of physics, University of California, Santa Barbara, California 93106, USA.
authors.forename: Zhen
authors.initials: Z
authors.lastname: Bi
authors.affiliation: Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802-6300, USA.
authors.forename: Ruixing
authors.initials: R
authors.lastname: Zhang
authors.affiliation: Department of physics, University of California, Santa Barbara, California 93106, USA.
authors.forename: Yi-Zhuang
authors.initials: YZ
authors.lastname: You
authors.affiliation: Department of physics, University of California, Santa Barbara, California 93106, USA.
authors.forename: Andrea
authors.initials: A
authors.lastname: Young
authors.affiliation: Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA.
authors.forename: Leon
authors.initials: L
authors.lastname: Balents
authors.affiliation: Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802-6300, USA.
authors.forename: Chao-Xing
authors.initials: CX
authors.lastname: Liu
authors.affiliation: Department of physics, University of California, Santa Barbara, California 93106, USA.
authors.forename: Cenke
authors.initials: C
authors.lastname: Xu