Manipulation of the surface density of states of Ag(111) by means of resonators: Experiment and theory

We show that the density of surface Shockley states of Ag(111) probed by the differential conductance $G\left(V\right)=dI/dV$ by a scanning-tunneling microscope (STM) can be enhanced significantly at certain energies and positions introducing simple arrays of Co or Ag atoms on the surface, in contrast to other noble-metal surfaces. Specifically we have studied resonators consisting of two parallel walls of five atoms deposited on the clean Ag(111) surface. A simple model in which the effect of the adatoms is taken into account by an attractive local potential and a small hybridization between surface and bulk at the position of the adatoms explains the main features of the observed $G\left(V\right)$ and allows us to extract the proportion of surface and bulk states sensed by the STM tip. These results might be relevant to engineer the surface spectral density of states, to study the effects of surface states on the Kondo effect, and to separate bulk and surface contributions in STM studies of topological surface states.

Figure 1

Topographic images of three Co resonators with atoms at $d_{Co\text{−}Co}=3a$. (a) 40-Co resonator with atomic walls at $d_w=7.6$ nm showing two maxima of the LDOS along the $\left[11\overline{2}\right]$ direction ($I_T=200$ pA, $V_{\mathrm{bias}}=50$ mV). (b) 20-Co resonator with walls at $d_w=5.4$ nm showing two maxima along the $\left[1\overline{1}0\right]$ closed packed direction ($I_T=200$ pA, $V_{\mathrm{bias}}=10$ mV). (c) 10-Co resonator with atomic walls built at $d_w=5.4$ nm. This atomic arrangement gives rise to a unique maximum along the $\left[1\overline{1}0\right]$ closed packed direction ($I_T=500$ pA, $V_{\mathrm{bias}}=10$ mV).

Figure 2

$dI/dV$ map at the Fermi level $\left(V=0\right)$ of Co resonators with atomic walls with different numbers of atoms and wall distances, $d_w$. (a) 40-Co resonator with $d_w=7.4$ nm (regulation set point: $I_T=200$ pA, $V=-100$ mV $V_{\mathrm{mod}}=3$ mV) showing an alternating maximum/minimum pattern of the Ag(111) LDOS along the $\left[1\overline{1}0\right]$ and the $\left[11\overline{2}\right]$ directions. (b) Conductance map at the Fermi energy of a 10-Co resonator with $d_w=5.4$ nm (regulation set point: $I_T=200$ pA, $V=-100$ mV; $V_{\mathrm{mod}}=3$ mV) showing only one maximum of the Ag(111) LDOS. (c) Line profiles along the $\left[1\overline{1}0\right]$ directions [dotted lines in (a) and (b)] showing a more intense maximum in the resonator with walls separated $d_w=5.4$ nm.

Figure 3

Theoretically calculated (left) and experimentally measured (middle) $G\left(0\right),V_{\mathrm{Onset}}$, and $V_{\mathrm{Max}}$ (see text) as the STM tip moves along the resonator for the first Co resonator (triangles), the second Co resonator (squares), and the Ag resonator (circles). The experimental data correspond to the line profiles measured in images (examples in the right panel) generated from a full differential conductance map taken at $V_{\mathrm{bias}}=-20$ mV, $I_T=500$ pA, and $V_{\mathrm{mod}}=1$ mV or a constant height image defined by a regulation set point $I_T=42$ pA, $V_{\mathrm{bias}}=-100$ mV on the bare Ag(111). The symbol and color code indicates data extracted from the same resonator.

Figure 4

Differential conductance as a function of voltage times electric charge $\left(\omega =eV\right)$ for the first Co resonator and two positions of the STM tip: near the center (red, peak nearest to $\omega =0$) and slightly outside the resonator (blue). Full (dashed) line correspond to experiment (theory, see text).

Figure 5

Theoretical differential conductance as a function of energy for the first Co resonator, the STM tip near the center (top) red, and slightly outside the resonator (bottom), and three different values of the potential $W$: $-0.342$ eV (dashed green line), $-0.402$ eV (full red line), and $-0.462$ eV (dot blue line). Full black line corresponds to experiment.

Figure 6

Differential conductance as a function of energy for the second Co resonator and two positions of the STM tip: near the center (red, peak nearest to $\omega =0$) and outside the resonator (blue). Full (dashed) line corresponds to experiment (theory).

Figure 7

Differential conductance as a function of energy for the Ag resonator and two positions of the STM tip: near the center (red, peak nearest to $\omega =0$) and slightly outside the resonator (blue). Full (dashed) line corresponds to experiment (theory).

Figure 8

Spectral density of surface states as a function of energy for the STM tip above one of the adatoms that form the Ag (full red line) and the first Co (dashed blue line) resonator. Dotted lines denote the result for a smaller $W_b=0.001$ meV. The inset shows the energy resolved $dI/dV$ spectra of single Ag and Co adatoms on Ag(111) taken at $V_{\mathrm{bias}}=-100$ mV, $I_t=200$ pA and $V_{\mathrm{bias}}=-100$ mV, $I_t=70$ pA, respectively. Both $dI/dV$ curves present the split-off bound state around 75 mV below the Fermi energy. In addition, the Co atom on Ag(111) spectra presents a second resonance near the Fermi level due to the Kondo effect.

Figure 9

Theoretical differential conductance as a function of energy for the Ag resonator and three distances $d$ of the STM tip to the center of the resonator: $d=10$ nm (dot red line), $d=20$ nm (dashed blue line), and $d\to \infty$ (full black line).

Figure 10

Full line: theoretical differential conductance as a function of energy for the STM tip in the center of the Ag resonator. Dashed line: the same for an Ag resonator with two times longer walls. Dotted line: the same for two infinite hard walls.

Figure 11

Full line: theoretical differential conductance as a function of energy for the STM tip in the center of the Ag resonator. Dashed line: the same for a hypothetical closed Ag resonator with five atoms per wall. Dotted line: the same for six atoms per wall. Vertical thin dotted lines correspond to eigenenergies of a hard-wall rectangular corral.