  We demonstrate gate-tunable resonant tunneling and negative differential
resistance in the interlayer current-voltage characteristics of rotationally
aligned double bilayer graphene heterostructures separated by hexagonal
boron-nitride (hBN) dielectric. An analysis of the heterostructure band
alignment using individual layer densities, along with experimentally
determined layer chemical potentials indicates that the resonance occurs when
the energy bands of the two bilayer graphene are aligned. We discuss the
tunneling resistance dependence on the interlayer hBN thickness, as well as the
resonance width dependence on mobility and rotational alignment.
