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We show theoretically that the tunnelling between properly designed defects in periodic antidot lattices can be strongly modulated by applied magnetic fields. Further, transport channels made up of linear arrangements of tunnel-coupled defects can accommodate Aharonov-Bohm cages, suggesting a magnetic control of the transport through the system. Evidence supporting an unusual robustness of the caging effect against electron-electron interactions is also provided.

Delocalized image surface states in free-standing hollow silica nanospheres populated with one or two electrons or an exciton are theoretically predicted for a wide range of internal radii and shell thicknesses. The driving force building up these surface states is the image self-polarization potential originating from the dielectric mismatch between the nanoshell and the surrounding air. The surface states are localized in a spherical crown beyond the nanoshell border. The transition from volume to surface state will then have to overcome the spatial confining potential barrier of the nanoshell. Owing to the different spatial confining barriers of electrons and holes in the silica nanoshell, electron but no hole density can be concentrated in surface distributions. The self-polarization potential looks like a double well potential, each well located just beyond the nanoshell border, with the internal well deeper than the external one, so that an excess carrier is attracted more strongly by the inner interface. This leads the electron density of a surface state to be located mainly in the internal surface of the hollow nanosphere. The shorter the inner nanoshell radius is, the stronger the binding of the excess electron to the surface will be. The volume/surface ground state phase diagrams of the one-electron, two-electron, and exciton systems have been calculated. All three diagrams are quite similar, thus revealing the monoelectronic character of the driving force for the transition from volume to surface states. [ABSTRACT FROM AUTHOR]

The band structure of a high-mobility two-dimensional electron gas patterned with a square lattice of holes (antidots) is studied theoretically under the influence of a magnetic modulation consisting of perpendicular magnetic flux tubes with the same period and nonzero net flux per unit cell. The magnetic field pierces the system through the patterned holes only, so that the coupling with the electrons is purely quantum mechanical. The model takes implicitly into account the coupling between the different Bloch bands. The flux-dependent energy structure exhibits a Hofstadter butterfly-type spectrum. Such a structure is repeated indefinitely without distortion with a period of one magnetic flux quantum through a lattice hole. Rectangular deviations from the square lattice are also studied. It is found that the number and width of the magnetic gaps decrease, and even disappear for large antidot filling fractions. [ABSTRACT FROM AUTHOR]