-based Heterostructures*

We investigate interlayer tunneling in heterostructures consisting of two tungsten diselenide (WSe₂) monolayers, separated by hexagonal boron nitride (hBN). In samples where the two WSe₂ monolayers are rotationally aligned, we observe resonant tunneling, manifested by a large interlayer tunneling conductance (σ_IL) and negative differential resistance near zero interlayer bias (V_IL), which stem from energy and momentum conserving tunneling. The strong spin-orbit coupling in monolayer WSe₂ splits the valence band and leads to coupled spin-valley degrees of freedom. To probe the role of spin-valley in the interlayer tunneling current-voltage characteristics, we investigate two WSe₂ layers separated by hBN with 0° and 180° relative twist between the WSe₂ layers. In the 0°-twist samples, a large σ_IL peak appears at V_IL = 0 V due to alignment of the like-valley-bands, i.e., the K valleys of the two WSe₂ layers. In the 180°-twist samples, in which the K and K’ valleys in opposite layers are aligned in momentum space, we observe a negligible σ_IL at V_IL = 0 V. Spin-valley conserved interlayer tunneling occurs when the like-valley-bands in the two layers are aligned, manifested as a large σ_IL at |V_IL| = ±0.5 V.