  We demonstrate gate-tunable resonant tunneling and negative differential
resistance between two rotationally aligned bilayer graphene sheets separated
by bilayer WSe2. We observe large interlayer current densities of 2 uA/um2 and
2.5 uA/um2, and peak-to-valley ratios approaching 4 and 6 at room temperature
and 1.5 K, respectively, values that are comparable to epitaxially grown
resonant tunneling heterostructures. An excellent agreement between theoretical
calculations using a Lorentzian spectral function for the two-dimensional (2D)
quasiparticle states, and the experimental data indicates that the interlayer
current stems primarily from energy and in-plane momentum conserving 2D-2D
tunneling, with minimal contributions from inelastic or non-momentum-conserving
tunneling. We demonstrate narrow tunneling resonances with intrinsic
half-widths of 4 and 6 meV at 1.5 K and 300 K, respectively.
