Photoemission Spectroscopy Using Virtual Photons Emitted by Positron Sticking: A Complementary Probe for Top-Layer Surface Electronic Structures

We present a spectroscopic method which utilizes virtual photons to selectively measure the electronic structure of the topmost atomic layer. These virtual photons are created when incident positrons transition from vacuum states to bound surface states on the sample surface and can transfer sufficient energy to excite electrons into the vacuum. The short interaction range of the virtual photons restricts the penetration depth to approximately the Thomas-Fermi screening length. Measurements and analysis of the kinetic energies of the emitted electrons made on a single layer of graphene deposited on Cu and on the clean Cu substrate show that the ejected electrons originate exclusively from the topmost atomic layer. Moreover, we find that the kinetic energies of the emitted electrons reflect the density of states at the surface. These results demonstrate that this technique will be a complementary tool to existing spectroscopic techniques in determining the electronic structure of 2D materials and fragile systems due to the absence of subsurface contributions and probe-induced surface damage.

Figure 1

(a) The Auger-mediated positron sticking (AMPS) process illustrated for single-layer graphene (SLG) on Cu: an incoming low-energy positron (red) sticks to SLG transferring its energy, via a virtual photon (VP) depicted in green, to an electron (blue) which now has sufficient energy to escape the material. (b) The first step. The emission of a VP as a result of a low-energy positron making a transition from a vacuum state to a bound surface state. The VP energy is $E_{\mathrm{VP}}=K{E}^{+}+{ϵ}_{\mathrm{SS}}$, where $K{E}^{+}$ is the positron kinetic energy and ${ϵ}_{\mathrm{SS}}$ is the surface state binding energy. (c) The VP is absorbed by an electron in the valence band providing sufficient energy to liberate the electron from the material with kinetic energy $K{E}^{-}=K{E}^{+}+{ϵ}_{\mathrm{SS}}-{ϵ}_1-{\varphi }^{-}$, where ${ϵ}_1$ is the electron binding energy and ${\varphi }^{-}$ is the electron work function.

Figure 2

The maximum energies of the AMPS electrons from Cu, $K{E}_{\max }^{-}$, as a function of the maximum virtual photon energies.

Figure 3

The measured AMPS spectra in black for maximum incident positron beam energies of 3.0, 4.5, and 5.5 eV shown alongside a modeled AMPS spectra in violet. Panels (a)–(c) are the results for SLG. Panels (d)–(f) are the results for Cu where the Cu AMPS spectra consist of a weighted sum of $4s\text{−}p$ (pink) and $3d$ (blue) partial AMPS spectra as described in the text. The kinetic energy which corresponds to the Fermi level is indicated by an orange arrow in each panel.