Corrugation induced stacking solitons with topologically confined states in gapped bilayer graphene

Graphene, as an atomic-thick ultrasoft membrane, almost has no resistance against out-of-plane deformations and, therefore, it is always wrinkled to a certain degree. Recently, corrugated structures and their effects on the electronic properties of monolayer graphene have been studied extensively. However, similar experimental studies in bilayer graphene have yet to be reported. Here, we show that corrugations in bilayer graphene can generate incommensurate stacking solitons (domain walls) between commensurate Bernal-stacked domains. By using scanning tunneling microscopy, we microscopically study electronic structures of a corrugation-induced stacking soliton that separates two adjacent AB and BA stacked bilayer regions with a uniform interlayer potential difference. Both topological gapless edge states and quasi-localized gapped quantum-well-like states are observed in the nanoscale corrugation. Atomic resolution mapping of the topological edge states along the stacking soliton reveals the existence of intervalley scattering between them, which could explain recent experiments where the conductance along domain walls of gapped graphene bilayer is smaller than a quantized value 4e2 h.