Experimental and theoretical study of the surface resonances on the (100) faces of W and Mo

Abstract

We present an experimental and theoretical study of the surface resonances on the (100) faces of W and Mo. From our experimental study, utilizing both angle-resolved photoemission with use of synchrotron radiation and angle-integrated photoemission, as well as field emission, we have documented the following properties of these surface resonances: (i) There are three occupied bands of surface resonances in the surface Brillouin zone. They are located about 0.2, 0.6, and 3.3 (0.3, 0.8, and 4.2) eV below the Fermi level for Mo (W). The dispersion is at most 0.3 eV for each band of surface resonances. (ii) The first band of resonances [at 0.2 (0.3) eV] is mainly $d_{z^2}$ in orbital character. It forms the well-known "surface-state" peak in the field-emission spectra. (iii) The second band of resonances is primarily composed of $d_{x^2-y^2}$ and $d_{zx,zy}$ orbitals. It results in a shoulder below the "surface-state" peak in both the field-emission and angle-integrated photoemission spectra. Its photoemission intensity is zero at normal exit. (iv) The third band of resonances is similar to the first one and also made up of $d_{z^2}$ and $s$ orbitals. (v) As far as we can tell, many-body effects are not required to explain any aspect of the photoemission results from these resonances. The experimental data are compared to our calculation of the ${\overrightarrow{\mathrm{k}}}_{\parallel }$- and orbital-resolved surface density of states, which uses a nonrelativistic tight-binding Green's-function scheme. The variations of the photoemission cross sections from these surface resonances are discussed in some detail and are shown to be determined by both macroscopic (i.e., the behavior of the electric field in the surface region, e.g., the reflection effects on the polarization vector) and microscopic (i.e., the details of the final-state band structure) effects.