The paper presents the results of a study of tunneling transport in macroscopic vertical van der Waals heterostructures based on bilayer graphene (BLG). The equilibrium tunneling conductivity was measured between two BLG sheets whose crystal lattices are rotated relative to each other by a small angle of ≈ Q ~ 0.7°, which imposes certain restrictions on the possibility of interlayer tunneling with energy and momentum conservation. The tunneling boundaries on the experimental conductivity map depending on the gate voltages are well described by the model, which takes into account the electrostatics of the system and tunneling at the Fermi level between the BLG sheets.

Anomalous in amplitude asymmetric peaks of conductivity were detected at the boundaries of the tunneling region, which we associate with the manifestations of van Hove singularities at the edges of the conduction band and the valence band near the gap formed in bilayer graphene under the influence of an electric field. The sharp asymmetry of such peaks is consistent with the spatial localization of van Hove singularities in different monolayers of bilayer graphene in a perpendicular electric field.

Schematic of dual-gated BLG/hBN/BLG device and measured map of tunneling conductance (in the center) as function top and bottom gate voltages. The tunneling is forbidden in the central part and displays prominent peaks near the charge neutrality points shown by dotted lines. Right and left pictures describe asymmetric situations from both sides of the charge neutrality: enhanced tunneling thanks to electron wave function in top BLG being pulled closer to the bottom BLG (right), and suppressed tunneling due to the opposite displacement of the wave function (left).

E.E.Vdovin et al.,
JETP Letters 120, issue 11 (2024)