Quasicrystalline Electronic States of a One-Dimensionally Modulated Ag Film

Ag films on GaAs(110) exhibit a one-dimensional quasiperiodic modulation, resulting in a Fibonacci sequence of parallel stripes with two different widths. Valence level photoemission shows that the Ag electronic states acquire a unique character along the quasiperiodic direction, distinctively manifested by a hierarchy of energy level replicas and avoided crossings at characteristic intervals in reciprocal space. These observations demonstrate the strong influence of the one-dimensional quasiperiodic potential on the Ag film states.

Figure 1

(a) LEED pattern of a 19 Å Ag film on GaAs(110) for 45 eV electron energy. (b) Schematic diagram of the LEED pattern in (a). The circles mark the position of the main spots: filled, unfilled, and unfilled small symbols represent spots of decreasing intensity. (c) LEED intensity along the central row of spots, showing the influence of two periodicities $k_a$ and $k_b$ on the diffraction pattern. (d) Photoemission intensity pattern at a binding energy of 0.3 eV below $E_{\mathrm{F}}$. The dominant set of concentric ellipses arises from the $s\mathrm{\text{−}}p$-derived quantum well states of the Ag film.

Figure 2

Sets of photoemission spectra recorded at a photon energy of 45 eV for different polar angles (a) along and (b) across the quasiperiodic stripe structure (see text).

Figure 3

Photoemission intensity plot for a wide range of reciprocal lattice vectors, (a) along and (b) across the quasiperiodic stripe structure. The reciprocal lattice vectors corresponding to $k_p$, $k_b$, and $k_b-k_a$ are indicated, together with the location of “quasizone boundaries” (QZBs).

Figure 4

Close-up spectra of the region around $(k_b-k_a)/2$, demonstrating the occurrence of several gaps between almost nondispersing states at QZB.