Direct observation of standing wave formation at surface steps using scanning tunneling spectroscopy

Decay of electronic excitations at metal surfaces

“…Noble-metal surface states have been the focus of experimental interest for over two decades, from their initial observation by angle-resolved photoemission spectroscopy by Gartland and Slagsvold [12] through to recent studies of defect scattering and lateral confinement on surface nanostructures [176][177][178][179][180]. The insight obtained from photoelectron spectroscopy has been reviewed in the preceding Section 3.…”

“…The wave functions of surface states have significant amplitude outside of a crystal, making it an ideal subject for STM which probes wave functions several Angstrom above a surface [176][177][178]. In particularly favorable cases, e.g.…”

“…It does not involve any other electron scattering yet. An additional, exponential damping of the scattered wave with a phase-relaxation length l can be introduced to mimic the effect of electron-electron or electron-phonon scattering (see Section 4.3.1) [177,184].…”

Direct observation of many-body charge density oscillations in a two-dimensional electron gas

“…Because of the wave-particle duality, electrons can interfere as shown by Davisson and Germer 1 . The invention of the scanning tunnelling microscope 2 (STM) allowed the visualization of this effect in the real space by looking at the spectacular standing wave patterns produced by elastic scattering of electrons and holes at surface defects, such as vacancies, adsorbates, impurities or step edges [3][4][5][6] . These waves, known as Friedel oscillations 7 , correspond to modulations of the electronic local density of states 8 (LDOS) and can be energetically resolved by differential conductivity (dI/dU) maps, usually measured at low temperature to reach a large coherence length and an improved energy resolution.…”

A non-perturbative treatment of quantum impurity problems in real lattices

“…The impurities are coupled through exchange interactions of different physical origins, either direct exchange for nearest-neighbor adsorption sites or indirect substrate-mediated coupling that asymptotically decay as a power-law with increasing separation between the impurities (RKKY interaction) [8][9][10]. The indirect exchange coupling depends on the nature of the substrate states involved: in addition to bulk states, some commonly used noble metal substrates, such as Cu (111), also have a band of surface states crossing the Fermi level [143,144].…”