  Heterostructures comprised of two two-dimensional electron systems (2DES)
separated by a dielectric exhibit resonant tunneling when the band structures
of both systems are aligned. It is commonly assumed that the height and width
of the resonant peak in the tunneling current is determined by electron
scattering and rotational misalignment of crystal structures of the 2DES. We
identify two fundamental factors limiting the maximum height and steepness of
the resonance: coupling to contacts and tunnel splitting of energy levels. The
upper limit of the tunneling current is the number of electrons available for
tunneling times half the tunnel coupling between the 2DES. As a result of a
tradeoff between the contact-induced level broadening and contact resistance,
the maximum current is only achievable when the coupling to contacts equals the
tunnel level splitting. According to our model calculations, the limiting
behavior can be observed in double-gated graphene/few-layer hexagonal boron
nitride/graphene heterostructures.
