Colloquium: Theory of quantum corrals and quantum mirages

Abstract

Quantum corrals are two dimensional structures built atom by atom on an atomically clean metallic surface using a scanning tunneling microscope (STM). These two dimensional structures "corral" electrons in the surface states of noble metals, leading to standing wave patterns in the electron density inside the quantum corral. We review the physics of quantum corrals and relate the signal of the STM to the scattering properties of substrate electrons from atomic impurities supported on the surface. The theory includes the effects of incoherent surface state electron scattering at the impurities and quantitively describes nearly all of the current STM data on quantum corrals, including the recent quantum mirage experiments with Kondo effect. We discuss the physics underlying the recent mirage experiments and review some of the outstanding questions regarding the Kondo effect from impurities in nanoscale structures on metallic surfaces. We also summarize recent work on variations of "quantum" corrals: optical corrals and acoustical corrals.

Colloquium: The spin-incoherent Luttinger liquid

“…͑8͒ and ͑11͒ ͑Fiete et al, 2006;Fiete and Kindermann, 2007;Iucci et al, 2007͒. The main result is that these correlations are exponentially suppressed when k B T տ E spin .…”

Theories of scanning probe microscopes at the atomic scale

“…Recent scanning tunneling microscopy studies of thin insulating films grown on conducting substrates (Glö ckler et al, 1996;Hebenstreit et al, 1999;Fö lsch et al, 2000) have motivated NC-SFM studies of similar surfaces. Specifically, high-quality atomic resolution was achieved on NaCl (001) films on copper substrates (Bennewitz et al, 1999a.…”

“…Of particular interest are studies of interference effects on surfaces due to scattering at step edges or atoms of a ''quantum corral'' (Heller et al, 1994;Bü rgi et al, 2000;Braun and Rieder, 2002;Fiete and Heller, 2003). The decay of the interference pattern, for example, with increasing distance from a step edge, is an indication of electron-electron and electron-phonon interactions, which reduce the phase memory of the electron.…”

Quantum mechanics writ large

“…Eddi et al (12) examined the interaction of a walker with a barrier and so developed a macroscopic version of quantum tunneling (19). Tunneling arises in quantum mechanics when a microscopic particle beats the odds by crossing a barrier, an effect that has recently led to a new generation of microscopes; for example, the scanning tunneling microscope has yielded unprecedented insights into the dynamics of electrons in confined geometries (20). In the experiments of Eddi et al (12), walkers are confined by four walls corresponding to vertical barriers, above which the droplets can bounce but not walk.…”