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.

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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.

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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)].

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All the essential switchable mirror properties of YHx exhibit a strong hysteresis that is related to the structural β-dihydride to γ-trihydride phase transition. This structural transition in YHx has so far been difficult to investigate since polycrystalline YHx films are optically homogeneous on the length scale of visible light wavelengths. However, in epitaxial YHx films the relation between local structural changes and local optical transmission can be investigated using in situ atomic force microscopy and optical microscopy, in hysteretic yttriumhydride mirrors exhibiting the earlier reported, domainwise pixel switching. We find widely varying local switching kinetics during the whole hydrogenation process. As a result, an epitaxial mirror forms essentially an ensemble of individual microcolumns, each of which can be in three regimes: (i) a single-phase regime of the β dihydride phase, where the optical transmission lowers with increasing hydrogen concentration, (ii) a layered two phase configuration in which the optical transmission rises with the fraction of high-concentration γ phase, and (iii) a single-γ-phase regime in which the transmission still increases significantly. The erect of a wide distribution of local properties on the global mirror properties are discussed within a simple model.@en

The kinetics of the metal-insulator transition in polycrystalline, Pd-capped YHx switchable mirrors upon hydrogenation is investigated. Using the accompanying optical transition, we study switching of matrix-like samples with many (∼200) combinations of Pd and Y layer thicknesses. We find that: (i) With increasing Y thickness dY, the switching time τ increases for any constant Pd thickness dPd. (ii) With increasing dPd, there are three regimes. In regime I, it is impossible to switch a device. This can mainly be related to Pd-Y compound formation consuming all Pd within the UHV system, followed by surface oxidation in air. In regimes II and III switching is possible, but only in regime III does Pd form a closed cap layer. The Pd thickness needed for a closed cap layer depends on dY. (iii) An oxide buffer layer hinders Pd-Y interdiffusion, so that a thinner Pd cap layer is needed for switching than in the case without buffer layer. This is interesting for potential applications since it yields a higher optical transmission in the open state of the device.@en

Switchable mirrors^1-3 made of thin films of the hydrides of yttrium (YH(x)), lanthanum (LaH(x)) or rare-earth metals exhibit spectacular changes in their optical properties as x is varied from 0 to 3. For example, α- YH(x<0.23) is a shiny, hexagonally close-packed metal, β-YH(2±δ) is a face-centred cubic metal with a blue tint in reflection and a small transparency window at red wavelengths, whereas hexagonally close-packed γ- YH(x>2.85) is a yellowish transparent semiconductor. Here we show that this concentration dependence of the optical properties, coupled with the high mobility of hydrogen in metals, offers the possibility of real-time visual observation of hydrogen migration in solids. We explore changes in the optical properties of yttrium films in which hydrogen diffuses laterally owing to a large concentration gradient. The optical transmission profiles along the length of the film vary in such a way as to show that the formation of the various hydride phases is diffusion-controlled. We can also induce electromigration of hydrogen, which diffuses towards the anode when a current flows through the film. Consequently, hydrogen in insulating YH(3-δ) behaves as a negative ion, in agreement with recent strong-electron-correlation theories^4,5. This ability to manipulate the hydrogen distribution (and thus the optical properties) electrically might be useful for practical applications of these switchable mirrors.

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