Lifetime of image-potential states on metal surfaces

Observing quantum trapping on MoS2 through the lifetimes of resonant electrons: revealing the Pauli exclusion principle

We demonstrate that the linewidth of the field emission resonance (FER) observed on the surface of MoS₂ using scanning tunneling microscopy can vary by up to one order of magnitude with an increasing electric field. This phenomenon originates from quantum trapping, in which the electron relaxed from a resonant electron in the FER is momentarily trapped in a potential well on the MoS₂ surface due to its wave nature. Because the relaxed electron and the resonant electron have the same spin, through the action of the Pauli exclusion principle, the lifetimes of the resonant electrons can be substantially prolonged when the relaxed electrons engage in resonance trapping. The linewidth of the FER is thus considerably reduced to as narrow as 12 meV. The coexistence of the resonant electron and the relaxed electron requires the emission of two electrons, which can occur through the exchange interaction.

Image-potential states and work function of graphene

Image-potential states of graphene on various substrates have been investigated by two-photon photoemission and scanning tunneling spectroscopy. They are used as a probe for the graphene-substrate interaction and resulting changes in the (local) work function. The latter is driven by the work function difference between graphene and the substrate. This results in a charge transfer which also contributes to core-level shifts in x-ray photoemission. In this review article, we give an overview over the theoretical models and the experimental data for image-potential states and work function of graphene on various substrates.

Lateral quantization of two-dimensional electron states by embedded Ag nanocrystals

We show that quantization of image-potential state (IS) electrons above the surface of nanostructures can be experimentally achieved by Ag nanocrystals that appear as stacking-fault tetrahedrons (SFTs) at Ag(111) surfaces. By means of cryogenic scanning tunneling spectroscopy, the n=1 IS of the Ag(111) surface is revealed to split up in discrete energy levels, which is accompanied by the formation of pronounced standing wave patterns that directly reflect the eigenstates of the SFT surface. The IS confinement behavior is compared to that of the surface state electrons in the SFT surface and can be directly linked to the particle-in-a-box model. ISs provide a novel playground for investigating quantum size effects and defect-induced scattering above nanostructured surfaces.

Probing quantized image-potential states at supported carbon nanotubes

Discrete image-potential states (ISs) are revealed at double-walled carbon nanotubes by means of scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) in the distance-voltage z(V) spectroscopy mode. The nanotubes are supported by flat Au(111) substrates. Due to the high sensitivity of the hot IS electrons to local variations of the surface potential, they can be considered as a sensitive probe to investigate interactions with the supporting substrate and impurities or defects at the nanotube surface. ISs provide information on the local electronic structure as well as on the electron dynamics at supported nanotubes.

Quantum confinement of hot image-potential state electrons

Discrete image-potential state (IS) resonances at Co nanoislands on Au(111) are probed using scanning tunneling microscopy and spectroscopy. We observe particle-in-box-type standing wave patterns, which is surprising in view of the high energy of the IS electrons when compared to the confining potential imposed by the island edges. The weak confining potential experienced by the IS electrons results in electronic interaction effects between closely spaced islands. Probing high-energy ISs hence provides a novel route to investigate electronic coupling between nanoislands on surfaces.

Highly extended image states around nanotubes

We predict that freely suspended, linear molecular conductors or dielectrics, such as carbon nanotubes, can support electronic states that are localized far from the surface. These "tubular image states" are formed in extended potential wells resulting from the tug of war between the external electron's attraction to its image charge in the nanotube, and its repulsion from the tube due to its transverse angular momentum. The displacement of these states (>10 nm) away from the surface prevents their wave functions from collapsing, resulting in long lifetimes at low temperatures. We predict that tubular image states with binding energies of 1-10 meV can be formed via radiative recombination.