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 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.

Bosonic topological insulator intermediate state in the superconductor-insulator transition

“…Our observation of a bosonic topological insulator in NbTiN and similar behavior in TDBG, stresses its universal character as a result of the Chern-Simons gap in the spectrum of relevant excitations. Note that the occurrence of bosonic topological insulator in the double belayered graphene is in a concert with the expectations of 22 . Interestingly, our previous findings of 35 support also the percolation network picture 36 of gapless bosonic channels near the BKT transition to TI.…”

Superconductivity from valley fluctuations and approximate SO(4) symmetry in a weak coupling theory of twisted bilayer graphene

“…This can be viewed as a trivial Z 2 topological order on top of a U(1) v × U(1) s bosonic symmetry protected topological (BSPT) state. [77,[94][95][96][97][98][99] The Z 2 topological order can be removed by condensing the charge neutral boson m. Then the Mott insulator simply realizes a U(1) v × U(1) s BSPT state with quantized valley-spin Hall conductance σ vsH = 1.…”

Metallic Phase and Temperature Dependence of the ν=0 Quantum Hall State in Bilayer Graphene

“…The FM state is a bulk insulator but possesses metallic quantum spin Hall (QSH) edge states [18,21]. The QSH edge states are a promising platform to examine the interactions of helical Luttinger liquid [28], and explore the potential realization of an interaction-driven bosonic symmetry protected topological state [29,30]. The pursuit of these intriguing possibilities requires substantial experimental knowledge of the FM (QSH) state, which is currently lacking.…”

“…The complex conductance behavior our measurements revealed makes it clear that understanding the conduction of the bulk FM state is a necessary part of probing the intrinsic behavior of the QSH edge states. Measurements at lower temperature using non-local transport geometries [40,41] or controlled tunneling at a quantum point contact will be essential to further explore the exciting prospects of the edge states in bilayer graphene [28][29][30].…”