We show that the spectrum of subbands in an electrostatically defined quantum wire in gapped bilayer graphene (BLG) directly manifests the minivalley structure and reflects Berry curvature via the associated magnetic moment of the states in the low-energy bands of this two-dimensional material. We demonstrate how these appear in degeneracies of the low-energy minibands and their valley splitting, which develops linearly in a weak magnetic field. Consequently, magnetoconductance of a ballistic point contact connecting two nongapped areas of a bilayer through a gapped (top and bottom gated) barrier would reflect such degeneracies by the heights of the first few conductance steps developing upon the increase of the doping of the BLG conduction channel (we consider an adiabatic constriction, where conductance is set by the number of propagating ballistic modes in its narrowest part): $8e^2/h$ steps in a wide channel in BLG with a large gap, $4e^2/h$ steps in narrow channels, all splitting into a staircase of $2e^2/h$ steps upon lifting valley degeneracy by a magnetic field.

• Received 10 August 2018
• Revised 28 September 2018

DOI:https://doi.org/10.1103/PhysRevB.98.155435