Practical electron cloaking in solids

Abstract

The design and experimental realization of "metamaterials" in the past decade has opened up new venues to obtain artificial materials with exotic properties that are desirable but not commonly encountered in the nature. Optical metamaterials have shown great potentials in applications such as optoelectronics, subwavelength imaging, and optical information processing etc. The invisibility effect, or "cloaking effect", is one of the most striking demonstrations of the unprecedented ability of manipulating light provided by optical metamaterials. As a natural extension, the cloaking effect of acoustic waves and quantum matter waves has also been discussed recently. Currently the main strategy of designing "cloaks" is the so-called transformation optics, and the resulting continuous distribution of material properties, such as the refractive index for optical metamaterials, the effective mass and the potential profile for matter-wave metamaterials, requires the artificial structures be much smaller than the wavelength of corresponding waves. In this thesis, the strategy of cloaking artificial scattering centers from conducting electrons in solids is discussed theoretically. The wavelength of conducting electrons in solids is of the order of a few nanometers, rendering the transformation optics technique impractical in this circumstance. Instead, a method based on the expansion of partial waves, analogous to the Mie theory for electromagnetic waves, is proposed. As an example, the design of "invisible" core-shell nanoparticles is demonstrated, and its application in thermoelectrics is discussed, where it is shown a simultaneous enhancement of the Seebeck coefficient and the electrical conductivity can be achieved. The corresponding formalism in 2D (both normal 2D electron gas system and graphene) is also derived, based on which novel electronic switches and filters can be constructed using properly designed gates to achieve desired potential profiles.