Surface state confinement in a lateral quantum well: The striped $\mathrm{Cu}\left(110\right)\left(2\times 1\right)\mathrm{O}$ surface

We report the response of the well-known Shockley-type surface state, which resides around $\overline{\mathrm{Y}}$ on the $\mathrm{Cu}\left(110\right)$ surface, to the presence of a lateral one-dimensional (1D) superlattice. This grating consists of alternating stripes of reconstructed $\mathrm{Cu}\left(110\right)\left(2\times 1\right)\mathrm{O}$ and unreconstructed $\mathrm{Cu}\left(110\right)$ and can be prepared by oxygen dosing over a wide range of stripe widths and distances, respectively. Using high-resolution angle-dependent photoemission at room temperature, we study the variation of binding energy, effective mass, linewidth and energy splitting induced by the confinement perpendicular to the $\left(2\times 1\right)\mathrm{O}$ stripes. We demonstrate that the surface state electrons on the striped $\mathrm{Cu}\text{−}\mathrm{O}$ surface show confinement properties and photoemission spectra in almost complete analogy to the $\overline{\Gamma }$-surface state electrons on stepped $\mathrm{Cu}\left(111\right)$ and $\mathrm{Au}\left(111\right)$ surface [Mugarza et al., Phys. Rev. Lett. 87, 107601 (2002)]. At low oxygen coverages our data differ from those of an earlier photoemission study of the same system performed with the sample at $100\mathrm{K}$ [Bertel and Lehmann, Phys. Rev. Lett. 80, 1497 (1998)], which reports the observation of singularities in the density of states of quasi-1D subbands. However, the two studies agree within experimental error limits for the higher oxygen coverages. We explain the apparent difference by the temperature-induced transition from coherent emission out of 2D superlattice bands to incoherent emission from decoupled 1D quantum well states.

Figure 1

Top: Atomic arrangement of the $\mathrm{Cu}\text{−}\mathrm{CuO}$ stripe phase formed by alternating stripes of $\mathrm{Cu}\left(110\right)$ (width L) and $\mathrm{Cu}\left(110\right)\left(2\times 1\right)\mathrm{O}$ (width l) resulting in a periodicity $\mathrm{D}=1+\mathrm{L}$ of the nanograting. Note that the $\mathrm{Cu}\text{−}\mathrm{O}$ chain length is large as compared to atomic distances. Bottom: crystal bulk axes (left) and surface Brillouin zone (right) for $\mathrm{Cu}\left(110\right)$. The dashed line shows the reduced zone (shaded) for the completely filled $\left(2\times 1\right)$ overlayer configuration $\left(\mathrm{L}=0\right)$.

Figure 2

Dispersion $E_i\left(k_{\Vert }\right)$ of the surface state around $\overline{\mathrm{Y}}$ on $\mathrm{Cu}\left(110\right)$ with $k_{\Vert }$ running along $\overline{\mathrm{Y}}-\overline{\mathrm{S}}$. Photon energy $\hslash \omega =21.2\mathrm{eV}$; sample at $300\mathrm{K}$. The solid line is a fit according to Eq. (1).

Figure 3

Low-energy electron diffraction patterns taken from the striped $\mathrm{Cu}\left(110\right)\left(2\times 1\right)\mathrm{O}$ surface at different oxygen coverages $\Theta$. The wave vector $k_{\Vert }$ (in units of the distance $2\overline{\Gamma X}$) is oriented perpendicular to the stripes. Sample at room temperature; electron kinetic energy $65.8\mathrm{eV}$.

Figure 4

(Non-)dispersion of the surface state along $\overline{\mathrm{Y}}-\overline{\mathrm{S}}$ between $\overline{\mathrm{Y}}\left(\varphi =0°\right)$ and $\varphi =12°$, where it leaves the projected bulk band gap around $\overline{\mathrm{Y}}$. Photon energy $\hslash \omega =21.2\mathrm{eV}$; angular resolution $\Delta \theta =\pm 0.7°$.

Figure 5

Surface state spectra taken along $\overline{\mathrm{Y}}-\overline{\mathrm{S}}$ from a surface with $\mathrm{L}=32\mathrm{\AA }$. Note that intensities are not drawn to scale, but are exaggerated for higher azimuthal angles $\varphi$ to make weak features better visible. Photon energy $\hslash \omega =8.3\mathrm{eV}\left(\mathrm{Xe}\mathrm{I}\right)$.

Figure 6

The same Fig. 5, but for a sample with $\mathrm{L}=46\mathrm{\AA }$. The bottom curves show the difference spectrum obtained by subtracting the $\varphi =0°$ spectrum from the $\varphi =-6°$ spectrum after appropriate normalization of intensities at $E_i=-0.4\mathrm{eV}$.

Figure 7

(a) Energy shift $E_1\left(\mathrm{L}\right)-E_0$ as a function of stripe width L, compare with Eq. (3) for a definition. Experimental data points are compared to result of the Kronig-Penney model (solid line) calculated with $V_0=0.7\mathrm{eV}$. (b) Energy difference $E_2-E_1$ in its dependence on L (data points) and a result of the Kronig-Penney model calculation (solid line, $V_0=0.7\mathrm{eV}$). (c) Experimental FWHM of the surface state peak at $\overline{\mathrm{Y}}$ as a function of L.

Figure 8

Energy eigenvalues calculated from the 1D Kronig-Penney model with a well depth of $V_0=0.7\mathrm{eV}$. The geometry parameters L and 1 correspond to Fig. 6.