Satellite band structure in silicon caused by electron-plasmon coupling

We report an angle-resolved photoemission measurement of the wave-vector-dependent plasmon satellite structure of a three-dimensional solid, crystalline silicon. In sharp contrast to nanomaterials, which typically exhibit strongly wave-vector-dependent low-energy plasmons, the large plasmon energy of silicon facilitates the search for a plasmaron state consisting of resonantly bound holes and plasmons and its distinction from a weakly interacting plasmon-hole pair. Employing a first-principles theory, which is based on a cumulant expansion of the one-electron Green's function and contains significant electron correlation effects, we obtain good agreement with the measured photoemission spectrum for the wave-vector-dependent dispersion of the satellite feature, but without observing the existence of plasmarons in the calculations.

Figure 1

(a) Experimental photoemission spectrum of silicon taken along $\varphi =-{30}^{\circ }$ (see the Appendix for definition of $\varphi$) using a photon energy of 711 eV. Here, $k_{\left|\right|}$ denotes the component of the electron wave vector parallel to the surface. (b),(c) Theoretical photoemission spectra from GW plus cumulant theory and GW theory, respectively, along $\varphi =-{30}^{\circ }$. (d),(e),(f) Same spectra as in (a), (b), and (c), but only the binding energy range relevant to the first satellite feature is shown.

Figure 2

(a) Experimental photoemission spectrum along $\varphi =-{60}^{\circ }$ (see the Appendix for a description of the experimental photoemission setup). (b),(c) Theoretical photoemission spectra from GW plus cumulant theory and GW theory, respectively. (d),(e),(f) Same spectra as in (a), (b), and (c), but only the binding energy range relevant to the first satellite is shown.

Figure 3

(a) Graphical solution of Dyson's equation for the lowest valence band of silicon at the $\Gamma$ point. The blue arrow denotes the plasmaron solution of the GW theory. (b) Spectral functions for the lowest valence band of silicon at the $\Gamma$ point from GW plus cumulant and GW theory. Arrows denote the position of the satellite peaks.

Figure 4

(a) Real-space geometry of the photoemission measurement. (b) Final-state wave vectors of electrons (red line) that reach the detector. The high-symmetry points of the Brillouin zone of silicon are labeled.

Figure 5

Comparison of the angle-resolved photoemission spectrum of silicon at different photon energies. Photon energies of 129 eV (a) and 711 eV (b) were used.