Bilayer Graphene as a platform for Bosonic Symmetry Protected Topological States

TL;DR

This paper proposes a feasible way to realize bosonic symmetry protected topological states in bilayer graphene under a magnetic field, highlighting the role of Coulomb interactions in creating protected edge states.

Contribution

It introduces a novel experimental platform in bilayer graphene for observing BSPT states, emphasizing the importance of Coulomb interactions in their formation.

Findings

Proposes bilayer graphene as a platform for BSPT states

Derives the bulk wave function matching the BSPT state

Suggests a bosonic quantum phase transition mechanism

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.