Charge-density oscillations on Be(101¯0): Screening in a non-free two-dimensional electron gas

The surface state on Be(101¯0) has been investigated using a low-temperature scanning tunneling microscope (STM). The Fermi contour of this surface state is located at one boundary of the surface Brillouin zone, and surface-state electrons provide the main part of the charge density near the Fermi energy. Be(101¯0), therefore, corresponds closely to a non-free two-dimensional electron gas. We have observed standing waves of the surface charge density on Be(101¯0) near step edges and point defects. Such wave patterns derive from the interference of incoming and scattered electrons; they demonstrate the screening characteristics of the surface state. On Be(101¯0) these waves were found to be highly anisotropic. It is shown that calculating the Fourier transforms of topographic STM images is a powerful method for determining the Fermi contour of the surface state. This method could even be applied to images that display a complex wave pattern arising from a random distribution of point scatterers. Fourier analysis also revealed that the charge density oscillations on Be(101¯0) contain multiple periods that differ by reciprocal lattice vectors. These multiperiodic oscillations relate to the non-free character of the surface-state electrons and constitute an interference pattern of Bloch states. Fourier filtering was used to separate the charge-density oscillations from the topographic corrugation and to visualize their shape and spatial range. The experimental data are qualitatively discussed using a model calculation based on the scattering of Bloch electrons from planar obstacles in a two-dimensional conductor. Experimental results and model calculations highlight how the screening characteristics on Be(101¯0) significantly deviate from the behavior expected for a free two-dimensional electron gas