Surface-state scattering by adatoms on noble metals: Ab initio calculations using the Korringa-Kohn-Rostoker Green function method

When surface-state electrons scatter at perturbations, such as magnetic or nonmagnetic adatoms or clusters on surfaces, an electronic resonance, localized at the adatom site, can develop below the bottom of the surface-state band for both spin channels. In the case of adatoms, these states have been found very recently in scanning tunneling spectroscopy experiments for the Cu(111) and Ag(111) surfaces. Motivated by these experiments, we carried out a systematic theoretical investigation of the electronic structure of these surface states in the presence of magnetic and nonmagnetic atoms on Cu(111). We found that Ca and all $3d$ adatoms lead to a split-off state at the bottom of the surface band which is, however, not seen for the $sp$ elements Ga and Ge. The situation is completely reversed if the impurities are embedded in the surface: Ga and Ge are able to produce a split-off state whereas the $3d$ impurities are not. The resonance arises from the $s$ state of the impurities and is explained in terms of strength and the interaction nature (attraction or repulsion) of the perturbing potential.

Figure 1

$s$ local density of states (LDOS) at the second vacuum layer above the Cu(111) surface. The full line represents the $s$ LDOS with the experimental lattice parameter and the dashed line refers to the $s$-LDOS with the LDA lattice constant.

Figure 2

LDOS at the second vacuum layer above the $3d$ adatoms $\left(2.86\mathrm{\AA }\right)$ on the Cu(111) surface. The full lines refer to majority-spin states, the dashed lines to minority-spin ones. The two arrows show the protrusions discussed in the text: (a) corresponds to a split-off state, (b) is a $d_{z^2}$ resonance.

Figure 3

$d$ contributions to the LDOS of $3d$ adatoms on the Cu(111) surface. The full lines describe the majority-spin states and the dashed lines describe the minority-spin states. Since the Cu adatom is nonmagnetic, the majority and minority virtual bond states coincide.

Figure 4

(Color online) Focus on the $s$-partial LDOS of the impurity atoms and $d_{z^2}$-partial LDOS reduced by a factor of 10. Black full lines represent the majority spin of $s$-partial LDOS, red (dark gray) dashed-dotted lines represent the majority spin of $d$-partial LDOS, black dashed lines describe the minority spin of $s$-partial LDOS, and red (dark gray) dotted lines describe the minority spin of $d$-partial LDOS.

Figure 5

(Color online) Variation of the scattering length $a$ versus the potential. Full lines correspond to a negative potential while the blue short-dashed line describes the case of positive potential (always repulsive). The figure is obtained for a small positive energy value and an elastic $s$ scattering by a rectangular spherical potential well of depth $V$ and radius $r_0$.

Figure 6

(Color online) LDOS in vacuum at the second layer above the impurities which are sitting in the surface layer. One can see the appearance of the split-off state above Ge impurities in a red (dark gray) full line but not above Co (black dotted-dashed line). Above the last one, a protrusion appears at $\approx -1.1\mathrm{eV}$ on the majority-spin channel which is due to the $d$ state of the Co impurity.