  We investigate interlayer tunneling in heterostructures consisting of two
tungsten diselenide (WSe2) monolayers with controlled rotational alignment, and
separated by hexagonal boron nitride. In samples where the two WSe2 monolayers
are rotationally aligned we observe resonant tunneling, manifested by a large
conductance and negative differential resistance in the vicinity of zero
interlayer bias, which stem from energy- and momentum-conserving tunneling.
Because the spin-orbit coupling leads to coupled spin-valley degrees of
freedom, the twist between the two WSe2 monolayers allows us to probe the
conservation of spin-valley degree of freedom in tunneling. In heterostructures
where the two WSe2 monolayers have a 180{\deg} relative twist, such that the
Brillouin zone of one layer is aligned with the time-reversed Brillouin zone of
the opposite layer, the resonant tunneling between the layers is suppressed.
These findings provide evidence that in addition to momentum, the spin-valley
degree of freedom is also conserved in vertical transport.
