Probing the features of electron dispersion by tunneling between slightly twisted bilayer graphene sheets

Tunneling conductance between two bilayer graphene (BLG) sheets separated by 2 nm-thick insulating barrier was measured in two devices with the twist angles between BLGs less than 1°. At small bias voltages, the tunneling occurs with conservation of energy and momentum at the points of intersection between two relatively shifted Fermi circles. Here, we experimentally found and theoretically described signatures of electron-hole asymmetric band structure of BLG: since holes are heavier, the tunneling conductance is enhanced at the hole doping due to the higher density of states. Another key feature of BLG that we explore is gap opening in a vertical electric field with a strong polarization of electron wave function at van Hove singularities near the gap edges. This polarization, by shifting electron wave function in one BLG closer to or father from the other BLG, gives rise to asymmetric tunneling resonances in the conductance around charge neutrality points, which result in strong sensitivity of the tunneling current to minor changes of the gate voltages. The observed phenomena are reproduced by our theoretical model taking into account electrostatics of the dual-gated structure, quantum capacitance effects, and self-consistent gap openings in both BLGs.