In van der Waals (vdW) materials, the electron mean free path (MFP) is largely influenced by the discrete states in the unoccupied band structure. So far, the influence of these states has only been measured in graphene, while all measurements on other vdW materials lack energy resolution. Here, we present reflection and transmission spectra of freestanding, few-layered molybdenum disulfide (MoS2) samples in the 0-55 eV electron range. Our measurements reveal states of enhanced electron transmissivity above the vacuum level, that correspond to the (unoccupied) density of states. We also show a full quantum-mechanical calculation that confirms a good understanding of the elastic scattering in MoS2. A model is developed to extract the inelastic MFP spectrum, which is a measure of the inelastic scattering cross section. As MoS2 is a complicated system of different atomic planes, we expect that our methods generalize well to other van der Waals materials and heterostacks thereof.

Although molecular rectifiers were proposed over four decades ago^1,2, until recently reported rectification ratios (RR) were rather moderate^2–11 (RR ~ 10¹). This ceiling was convincingly broken using a eutectic GaIn top contact¹² to probe molecular monolayers of coupled ferrocene groups (RR ~ 10⁵), as well as using scanning tunnelling microscopy-break junctions^13–16 and mechanically controlled break junctions¹⁷ to probe single molecules (RR ~ 10²–10³). Here, we demonstrate a device based on a molecular monolayer in which the RR can be switched by more than three orders of magnitude (between RR ~ 10⁰ and RR ≥ 10³) in response to humidity. As the relative humidity is toggled between 5% and 60%, the current–voltage (I–V) characteristics of a monolayer of di-nuclear Ru-complex molecules reversibly change from symmetric to strongly asymmetric (diode-like). Key to this behaviour is the presence of two localized molecular orbitals in series, which are nearly degenerate in dry circumstances but become misaligned under high humidity conditions, due to the displacement of counter ions (PF₆ ^–). This asymmetric gating of the two relevant localized molecular orbital levels results in humidity-controlled diode-like behaviour.

We investigate inelastic cotunneling in a model system where the charging island is connected to the leads through molecules with energy-dependent transmission functions. To study this problem, we propose two different approaches. The first is a pragmatic approach that assumes Lorentzian-like transmission functions that determine the transmission probability to the island. Using this model, we calculate current versus voltage (IV) curves for increasing resonance level positions of the molecule. We find that shifting the resonance energy of the molecule away from the Fermi energy of the contacts leads to a decreased current at low bias, but as bias increases, this difference decreases and eventually inverses. This is markedly different from IV behavior outside the cotunneling regime. The second approach involves multiple cotunneling where also the molecules are considered to be in the Coulomb blockade regime. We find here that when Ec≫eV,kBT, the IV behavior approaches the original cotunneling behavior proposed by Averin and Nazarov [Phys. Rev. Lett. 65, 2446-2449 (1990)].