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 $U(1)\times U(1)$ 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 bosonic nature of the boundary states, we derive the bulk wave function for the bosonic charge and spin degrees of freedom, which takes exactly the same form as the desired BSPT state. We also propose that the bulk quantum phase transition between the BSPT and trivial phase, could 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 which occur for free fermion systems. We discuss various experimental consequences of this proposal.

9 pages, 5 figures

References in corpus (9)

• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• The Helical Liquid and the Edge of Quantum Spin Hall Systems
• Spin Filtered Edge States and Quantum Hall Effect in Graphene
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Kondo effect in the helical edge liquid of the quantum spin Hall state
• Evidence for a Spin Phase Transition at ν=0 in Bilayer Graphene
• Edge excitations of the canted antiferromagnetic phase of the $\nu =0$ quantum Hall state in graphene: a simplified analysis
• Quantum Phase Transitions Between Bosonic Symmetry Protected Topological States Without Sign Problem: Nonlinear Sigma Model with a Topological Term
• Bridging Fermionic and Bosonic Short Range Entangled States

Cited by in corpus (15)

• Superconductivity from Valley Fluctuations and Approximate SO(4) Symmetry in a Weak Coupling Theory of Twisted Bilayer Graphene
• Breakdown of topological Thouless pumping in the strongly interacting regime
• From Bosonic Topological Transition to Symmetric Fermion Mass Generation
• Bosonic topological insulator intermediate state in the superconductor-insulator transition
• Metallic Phase and Temperature Dependence of the $\nu =0$ Quantum Hall State in Bilayer Graphene
• Higher-Order Topological Mott Insulator on the Pyrochlore Lattice
• Interacting topological mirror excitonic insulator in one dimension
• Generic "Unnecessary" Quantum Critical Points with Minimal Degrees of Freedom
• Lattice realization of a bosonic integer quantum Hall state - trivial insulator transition and relation to the self-dual line in the easy-plane NCCP1 model
• Minimal Fractional Topological Insulator in half-filled conjugate moiré Chern bands
• Interacting Valley Chern Insulator and its Topological Imprint on Moiré Superconductors
• Higgs Condensates are Symmetry-Protected Topological Phases: II. $U(1)$ Gauge Theory and Superconductors
• Topology- and symmetry-protected domain wall conduction in quantum Hall nematics
• Fingerprints of bosonic symmetry protected topological state in a quantum point contact
• Bosonic SET to SPT Transition under Dyonic LSM Theorem