Direct Probing of the Electronic Structures of Single-Layer and Bilayer Graphene with a Hexagonal Boron Nitride Tunneling Barrier.

The chemical and mechanical stability of hexagonal boron nitride (h-BN) thin films and their compatibility with other free-standing two-dimensional (2D) crystals to form van der Waals heterostructures make the h-BN-2D tunnel junction an intriguing experimental platform not only for the engineering of specific device functionalities but also for the promotion of quantum measurement capabilities. Here, we exploit the h-BN-graphene tunnel junction to directly probe the electronic structures of single-layer and bilayer graphene in the presence and the absence of external magnetic fields with unprecedented high signal-to-noise ratios. At a zero magnetic field, we identify the tunneling spectra related to the charge neutrality point and the opening of the electric-field-induced bilayer energy gap. In the quantum Hall regime, the quantization of 2D electron gas into Landau levels (LL) is seen as early as 0.2 T, and as many as 30 well-separated LL tunneling conductance oscillations are observed for both electron- and hole-doped regions. Our device simulations successfully reproduce the experimental observations. Additionally, we extract the relative permittivity of three-to-five layer h-BN and find that the screening capability of thin h-BN films is as much as 60% weaker than bulk h-BN.