Layered opposite Rashba spin-orbit coupling in bilayer graphene: Loss of spin chirality, symmetry breaking, and topological transition

Inversion symmetry in bilayer graphene allows for layered opposite Rashba spin-orbit coupling (LO-RSOC) -- the situation when RSOC has same magnitude but sign two coupled spatially separated layers. We show that LO-RSOC results loss of spin chirality momentum space, contrast to common uniform RSOC. This makes it difficult experimentally establish whether (on scale 10 meV) exists, because band structure is insensitive it. To solve this problem, we propose identify either by gating break inversion or magnetic field time-reversal symmetry. Remarkably, observe transition between trivial and non-trivial topology as system deviates from LO state. Ab inito calculations suggest encapsulated monolayers Au a candidate be system.