Gold conduction-band dispersion diagram (orange), along with the energy–momentum region occupied by graphene electrons (light blue), involving a bias energy e V b as well as the gold and graphene Fermi energies EF^Au and EF^g , respectively, out-of-plane electron energy in gold at the Fermi level, EF^⊥ . As a function of k ∥ , the out-of-plane gold Fermi surface (dashed orange parabola) has a minimum energy mismatch (that is, a maximum spill-out of gold electrons towards the hBN barrier) at the Γ point. The two considered tunnelling channels bridge the energy–momentum mismatch between the graphene K point and gold Fermi energy at k ∥ = 0. The direction of k∥ in b is along the radial dashed line in a .
