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We show that delaminations in bilayer graphene (BLG) with electrostaticallyinduced interlayer asymmetry can provide one with ballistic channels forelectrons with energies inside the electrostatically induced BLG gap. Thesechannels are formed by a combination of valley-polarised evanescent statespropagating along the delamination edges (which persist in the presence of astrong magnetic field) and standing waves bouncing between them inside thedelaminated region (in a strong magnetic field, these transform into Landaulevels in the monolayers). For inverted stacking between BLGs on the left andright of the delamination (AB-2ML-BA or BA-2ML-AB), the lowest energy ballisticchannels are gapless, have linear dispersion and appear to be weaklytopologically protected. When BLG stacking order on both sides of thedelamination is the same (AB-2ML-AB or BA-2ML-BA), the lowest energy ballisticchannels are gapped, with gap $\varepsilon_g$ scaling as $\varepsilon_g\proptoW^{-1}$ with delamination width and as $\varepsilon_g\propto\delta^{-1}$ withthe on-layer energy difference within the delamination. Depending on theirwidth, delaminations may also support several `higher energy' waveguide modes.Our results are based on both an analytical study of the wavematching of Diracstates and tight binding model calculations, and we analyse in detail thedependence of the delamination spectrum on electrostatic conditions in thestructure, such as the vertical displacement field.

Ballistic electron channels including weakly protected topological states in delaminated bilayer graphene