Surface electronic structures of La(0001) and Lu(0001)

Most spectroscopic methods for studying the electronic structure of metal surfaces have the disadvantage that either only occupied or only unoccupied states can be probed, and the signal is cut at the Fermi edge. This leads to significant uncertainties, when states are very close to the Fermi level. By performing low-temperature scanning tunneling spectroscopy and ab initio calculations, we study the surface electronic structures of La(0001) and Lu(0001), and demonstrate that in this way detailed information on the surface electronic structure very close to the Fermi energy can be derived with high accuracy.

Figure 1

(a) Tunneling spectrum of La(0001) at $T=10\mathrm{K}$ (rotated) and calculated band structure of a relaxed 11-layer La(0001) film. Surface states are marked by filled circles, bulk states by open circles. The most pronounced peak in the STS data at around $0.1\mathrm{eV}$ is attributed to the narrow surface-state band around the $\overline{\Gamma }$ point of the surface Brillouin zone. (b) Tunneling spectrum of Lu(0001) at $T=10\mathrm{K}$ and corresponding band structure of a relaxed 12-layer Lu(0001) film. The surface state appears as a sharp peak at $E_F$ in STS.

Figure 2

Highly resolved tunneling spectrum of La(0001) at $T=10\mathrm{K}$ and least-squares fit (gray line) composed of a surface-state line according to Eqs. (1, 2, 3) (dashed) and a quadratic background (dash-dotted line) to account for tunneling into bulk states. The residual of the fit is shown as a thin dotted line.

Figure 3

Highly resolved tunneling spectrum of Lu(0001) at $T=10\mathrm{K}$ and least-squares fit (gray line) composed of a surface-state line according to Eqs. (1, 2, 3) (dashed line) and a quadratic background (dash-dotted line) to account for tunneling into bulk states. The residual of the fit is shown as a thin dotted line.

Figure 4

(a) Same tunneling spectrum of Lu(0001) as in Fig. 3. The gray line represents a least-squares fit composed of a surface-state line according to the present model [Eq. (7)] (dashed) and a quadratic background (dash-dotted) to account for tunneling into bulk states. The residual of the fit is shown as a thin dotted line. (b) Dispersion and density of states of the Lu surface band, and (c) energy-dependent lifetime width resulting from the fit analysis. The gray-shaded area marks the uncertainty region for the estimation of $\Gamma$ (for details, see text).