Electron confinement in hexagonal vacancy islands: Theory and experiment

Electron confinement in hexagonal vacancy islands on Cu(111) is studied by state of the art ab initio calculations and experimentally by low-temperature scanning tunneling spectroscopy measurements (STS). Both theory and experiment reveal standing wave patterns of the local density of states (LDOS), which are ascribed to the scattering of surface-state electrons at the boundary of the vacancy island. The spatial modulation of the LDOS, its size, and energy dependence as measured by STS are well reproduced by our calculations. This agreement between theory and experiment corroborates the application of our theoretical approach to other confined systems, including spin-polarized effects. Our studies predict that quantum states of vacancy islands with magnetic adatoms can be used to tailor the spin-polarization of surface-state electrons on metal surfaces.

Figure 1

(Color) (a) Topographic STM image of a $7\mathrm{nm}$ size vacancy island on Cu(111) ($U_{\text{gap}}=-0.02\mathrm{V}$, $I=0.5\mathrm{nA}$). The line scans of (b) are given by the lines. (b) The line scans reveal the monolayer deep depression $\left(0.21\mathrm{nm}\right)$ and two apparent modulations (arrows) due to the impact of the electron standing waves on the topographic image. The depression has a size of $7\mathrm{nm}$, which varies by $\sim 0.1–0.2\mathrm{nm}$, along different scan directions. (c) A corral of Cu adatoms on Cu(111) with the same size $d$ as the depression is used in the calculations to model the vacancy island of (a).

Figure 2

(Color) STS images of $dI∕dU$ at the indicated gap voltage at $1\mathrm{nA}$ (left column) and the calculated LDOS at various energies of the $7\mathrm{nm}$ vacancy island of Fig. 1. The solid hexagon marks the vacancy island rim as in Fig. 1. The right column shows horizontal line scans along the center of the vacancy island, as indicated by the green line for different energies. Solid line: calculation (center column), symbols: experimental data (left column).

Figure 3

(Color) Left column: STS images of vacancy islands of different size of $4.3–10.6\mathrm{nm}$ as indicated on the center column plots, at various $U_{\text{gap}}$, as given on the left column $(I=1\mathrm{nA})$. Center column: Spectroscopy $dI∕dU$ at center position of the vacancy islands (stabilization parameters: $U_{\text{gap}}=-1\mathrm{V}$, $1\mathrm{nA}$). Right column: calculated LDOS spectra. The arrows indicate the energy levels $E_n$ as adopted from an analytical model (Ref. 20). With increasing vacancy island size, more energy levels appear that correspond to the levels $n=1,4,10,13,20,26,32$, with increasing energy.

Figure 4

(Color) Magnetic mirages in the vacancy island. A magnetic Co adatom is placed at the center of the vacancy island with $R=6.64\mathrm{nm}$. $N$ ↑ and $N$ ↓ are the LDOS for majority and minority electrons. $\Delta N$ ↓ and $\Delta N$ ↑ are determined by the difference between LDOS at the energy $E_F$ between the vacancy island with the Co adatom and the empty vacancy island.