Elementary Excitations I: Single Electronic Quasiparticles
Surfaces are many-body systems consisting of interacting cores and electrons (Sect. 3.3.1). In order to describe many properties, in particular, groundstate properties, it is sufficient to replace the system of interacting electrons by a system of indepen
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5.1 Electrons and Holes 5.1.1 Excitation and Quasiparticle Character Surfaces are many-body systems consisting of interacting cores and electrons (Sect. 3.3.1). In order to describe many properties, in particular, groundstate properties, it is sufficient to replace the system of interacting electrons by a system of independent particles (3.2). One example is the density functional theory (Sect. 3.4.1) within the local approximation for the exchange and correlation contribution to the total energy (3.50). Using the Kohn– Sham equation (3.46), the ground state of the electronic subsystem can be described by independent (i.e., effectively non-interacting) particles, more strictly electrons moving in an effective single-particle potential (3.48). An ‘independent’ electron in a Kohn–Sham state possesses a fixed single-particle energy and a defined probability distribution of finding this electron in space. However, excitations of an electronic system cannot correctly be described by the independent Kohn–Sham particles in (3.46). A lot of experimental studies are associated with spectroscopies and, therefore, excitations of the electronic (sub)system. An electron may be added to the system or an electron may be taken away from the system and, hence, a hole is created. The excited electron or the hole strongly interacts with the many other electrons of the system. The electronic subsystem is polarized and reacts with a redistribution of the electron density. Consequently, the energy of such an electronic excitation will differ from those for non-interacting particles. It is renormalized with respect to energy and to behavior in time, i.e., to the spectral distribution. If an excitation has a sufficiently long lifetime, it however behaves like a particle. Therefore, it is called a quasiparticle, more strictly a quasielectron or quasihole depending on the occupation of the corresponding single-particle state before excitation. The properties of the quasiparticle are better described by a spatially non-local spectral(-weight) function than by an eigenenergy and a wave function. Such quasiparticles are actually observable in several surface-sensitive spectroscopies.
F. Bechstedt, Principles of Surface Physics © Springer-Verlag Berlin Heidelberg 2003
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5. Elementary Excitations I: Single Electronic Quasiparticles
5.1.2 Scanning Tunneling Spectroscopy The first scanning tunneling microscope was built in 1982 by Binnig and Rohrer [5.1]. The physical phenomenon at the origin of this new instrument is the tunneling of electrons through the vacuum. In such a microscope a sharp metallic tip is positioned at a distance d (of the order of a few ˚ A) from the surface of a conducting sample (Fig. 5.1). In this way there is an overlap between the electronic wave functions of the tip and substrate. A voltage V is applied to the two electrodes resulting in a tunnel current IT . This can occur from the metal tip to the surface or vice versa, depending on the direction of the bias. Structural information can be obtained by scanning, i.e., by mov
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