Fig. 3: Resonant inelastic tunnelling spectroscopy of delicate features in electronic density of states of emitter and collector layers.

a Experimental differential tunnelling conductance at \(T=2\) \({\rm{K}}\) as a function of bias (\({V}_{{\rm{b}}}\)) and backgate (\({V}_{{\rm{bg}}}\)) voltages at fixed topgate voltage of \({V}_{{\rm{tg}}}=4\,{\rm{V}}\). Insert illustrates the schematic band diagram corresponding to the forbidden tunnelling event presented in a zoomed map in (c) and evaluated in (d). The tunnelling conductance values are normalized over the cross-sectional area of Device 1 (\(S\approx 20\,{ \mu}{{ \rm{m}}}^{2}\)). b Evaluated differential tunnelling conductance maps corresponding to inelastic tunnelling as a function of bias (\({V}_{{\rm{b}}}\)) and backgate (\({V}_{{\rm{bg}}}\)) voltages at fixed topgate voltage of \({V}_{{\rm{tg}}}=4\,{\rm{V}}\). The white dashed lines correspond to the alignments of chemical potentials of moiré monolayer and Bernal bilayer graphene electrodes with their neutrality points, and the alignment of the chemical potential of moiré monolayer graphene with valence band second neutrality point arising from its alignment with encapsulating hBN layer. Insert illustrates the schematic band diagram corresponding to the forbidden tunnelling event presented in a zoomed map (e) and evaluated map (f). c–f Zoomed-in regions of experimental (a) and theoretical (b) differential tunnelling conductance maps corresponding to resonant features associated with the twist-angle in moiré monolayer graphene of approximately 1° with a valence band bandgap of \({\Delta }_{2{\rm{NP\mbox{-}Gr}}}=\) 7 \(\,{\rm{meV}}\) (c–d), and with the electric-field induced bandgap of \({\Delta }_{{\rm{BGr}}}=\) 42\(\,{\rm{meV}}\) of Bernal bilayer graphene (e–f).