How can you locate valence electrons in a material? A scanning tunneling microscope can do so with atomic resolution, but it’s only sensitive to electrons on the surface of a material. Light can penetrate deeper, but its resolution is limited by its wavelength. To reach atomic resolution with light, researchers must use x rays, which are less sensitive to valence electrons than visible light. Now Eleftherios Goulielmakis of the University of Rostock in Germany and his colleagues have designed a visible-light imaging technique with resolution of tens of picometers that works for the valence electrons in a crystalline material. The trick is measuring the high harmonics produced by the crystal when it’s irradiated by an intense laser.
After the valence electrons are struck by a laser pulse that is about as energetic as the crystal potential, they move like quasi-free electrons driven by the laser’s electric field. As the intensity of the laser is increased, the crystal potential (gray line just under magenta one in first figure) is suppressed more and more until it disappears (orange line) at the critical field.
At that point, the crystal potential can be treated as a small perturbation to the electrons’ laser-driven motion. And nonlinear scattering is sensitive to that perturbation. The laser-driven electrons oscillate and emit light at multiples of the laser’s frequency whenever they slow down. The intensity of the resulting set of harmonics as a function of the laser’s strength can be transformed into a one-dimensional picture of the crystal potential in the direction of the laser’s polarization.
Goulielmakis and his colleagues studied a magnesium fluoride crystal irradiated by a visible laser with fields from 0.4 to 0.7 V Å–1. With the reconstructed potential, they derived the electron density (see the second figure) and the distance from the atoms’ nuclei to their outermost valence electrons, or the valence radii. For the Mg+2 ions, they obtained a 76 pm radius, in reasonable agreement with the accepted value of 72 pm. The researchers also compared their results on MgF2 with those of calcium fluoride. The changes in the radii of Mg, F, and Ca indicated the expected transfers of electrons, and MgF2 had low electron density between the ions, as expected for ionic bonds.
The natural next step is incorporating both spatial and time resolution. The equipment required for Goulielmakis and his team’s measurement can be easily incorporated into a time-resolved setup with attosecond resolution. Such a measurement could provide detailed information about phase transitions. (H. Lakhotia et al., Nature 583, 55, 2020; thumbnail image credit: University of Rostock.)
