Mode-selective electron-phonon coupling in laser photoemission on Cu(110)

By combining density functional perturbation theory (DFPT) calculations and laser photoemission spectroscopy (LPES) experiments, we have clarified the selective coupling between low-energy photoelectrons and subsurface phonon modes. A step structure resulting from the inelastic scattering of photoelectrons appeared at 14.7 meV below the Fermi level in the LPES of Cu(110). We found that the inelastic step originates from an indirect excitation in which the electron is excited by the low-energy photon near the $\overline{\mathrm{Y}}$ point and then scattered to the $\overline{\Gamma }$ point by phonon modes that are predominantly present in the subsurface region.

Figure 1

(a) (Top) LPES of the clean Cu(110) surface excited by the laser photon from 4.571 to 5.021 eV. The sample temperature is 16 K. The inelastic component is evaluated by deconvoluting the spectrum into two individual Fermi-Dirac distribution functions. The center of the Fermi-Dirac distribution function of the inelastic component is 14.7 meV below ${\mathrm{E}}_{\mathrm{F}}$, and the intensity of the inelastic component depends on the laser energy. (Bottom) First derivative spectrum excited by 4.571 eV photon. The curve has been smoothed to decrease the noise level in the derivative spectrum. (b) Calculated electronic band structure of Cu(110). A Shockley-type surface state appears around the $\overline{\mathrm{Y}}$ point near ${\mathrm{E}}_{\mathrm{F}}$. Insets are the top view of the slab model and surface Brillouin zone of Cu(110), respectively. (c) Schematic diagram of the indirect excitation in LPES. (d) Calculated phonon band structure of Cu (110).

Figure 2

(a) Calculated electron-phonon coupling matrix element $\langle {\psi }_{0c}\left|V_p(q,i,r)\right|{\psi }_{q\alpha }\rangle$ with a phonon energy of 14.7 meV, which induces photoelectron scattering from the $k$ point with wave vector $q$ to the $\overline{\Gamma }$ point. To reproduce the low-energy photoelectron, we use the energy of ${\mathrm{E}}_{\mathrm{V}}$ as the energy of photoelectron. The $k$ point is sampled at 16 irreducible points in a $6\times 6\times 1$ mesh of the first Brillouin zone. In order to extract the contribution from the electronic state near ${\mathrm{E}}_{\mathrm{V}}$, we multiply $\delta (E_{\alpha }-E_v)$ which is approximated by the Gaussian function of $\sqrt{2\ln \left(2\right)}\times 50$ meV half width at half maximum (HWHM). Original discrete matrix elements are smeared by using the Gaussian function of $\sqrt{2\ln \left(2\right)}$ meV HWHM to treat electron-phonon coupling as a function of phonon energy. (b) Electron-phonon coupling spectrum at the $\overline{\mathrm{Y}}$ point as a function of the phonon energy. The spectrum shows a main peak around 15 meV phonon energy, which describes well the single inelastic step structure in the LPES on Cu(110). (c) Calculated electron-phonon coupling at ${\mathrm{E}}_{\mathrm{V}}$ as a function of the phonon energy that scatters the photoelectron from each $k$ point to the $\overline{\Gamma }$ point. The calculation results include the contribution from the whole modes that exist at each $k$ point. The $k$ point is sampled at 16 irreducible points (labeled q1–q16) in a $6\times 6\times 1$ mesh of the first Brillouin zone. The inset shows the coordination of irreducible points in the surface Brillouin zone.

Figure 3

The charge distribution of electronic states around ${\mathrm{E}}_{\mathrm{F}}$ and ${\mathrm{E}}_{\mathrm{V}}$ at (a) the $\overline{\Gamma }$ and (b) the $\overline{\mathrm{Y}}$ point, respectively. The product between the charge distribution around ${\mathrm{E}}_{\mathrm{F}}$ and ${\mathrm{E}}_{\mathrm{V}}$ is also shown. The color shows the summation of charge density projected onto the (001) surface. Red and blue indicate higher and lower values of the charge density, respectively. The dotted circle in each plot indicates the position of the Cu atoms. At the $\overline{\mathrm{Y}}$ point, the electronic state closest to ${\mathrm{E}}_{\mathrm{F}}$ is the Shockley surface state. Note that the “surface” state penetrates into the subsurface layer. The charge distribution of the Shockley surface state and bulk state at ${\mathrm{E}}_{\mathrm{V}}$ overlap in the interior of Cu. In contrast, at the $\overline{\Gamma }$ point, the charge distribution of the electronic state near ${\mathrm{E}}_{\mathrm{F}}$ and ${\mathrm{E}}_{\mathrm{V}}$ exhibits minor overlap. These figures are rendered with VESTA.[34]

Figure 4

The distribution of atomic displacement from four phonon modes polarized along the [$\overline{1}10$] direction which couple with the photoelectron strongly at ${\mathrm{E}}_{\mathrm{V}}$ at the $\overline{\mathrm{Y}}$ point. $\omega$ is the phonon energy. The displacement in this figure is the absolute value of the projection onto the [$\overline{1}10$] direction. In all four modes, the atomic displacement is large in the subsurface region, which indicates that these modes are subsurface phonon modes.