Extended Data Fig. 3: DFT-NEGF-simulated spectral current (in absolute units), | J(E)|, along the transport direction (x) in the Nb_0.3W_0.7Se₂/WSe₂ heterostructure of Fig. 4c for different N_A,WSe2 doping concentrations in the WSe₂ bottom layer a. N_A,WSe2 = 3×10¹²cm⁻², b. N_A,WSe2 = 6×10¹²cm⁻², and c. N_A,WSe2 = 1.8×10¹³cm⁻².

The valence band in the WSe₂ layer, E_V,WSe2, as well as, the source Fermi level in the Nb_0.3W_0.7Se₂ metallic region (black dotted line), E_{FS, metal}, are also indicated. The x-distance between the end of the E_FS,metal line and the E_V,WSe2 line in the vicinity of the source Fermi level L_t,SBH is indicated with a blue arrow in a. L_t,SBH represents an estimate of the carrier tunneling distance through the Schottky barrier. As N_A,Wse2 is increased, this distance is strongly reduced b, or vanishes c, that is, the carriers feel an increasingly transparent Schottky barrier when crossing from the edge of the metal layer to the WSe₂ layer. Finally, the position of the neutrality level, E_N,metal, that is, the equilibrium DFT- Fermi-level moved by the self-consistent potential in the metal layer is also shown, as well as a schematic view of the device, with the top metal and bottom WSe₂ positions in the x-direction matching those of the spectral plot. V_DS = −0.15 V.