QUANTUM MAGNETIC CONFINEMENT IN A CURVED 2-DIMENSIONAL ELECTRON-GAS

The ability to produce deliberately shaped or curved two-dimensional electron gases in semiconductors using recent developments in technology, for example regrowth of III-V semiconductors on patterned or etched substrates, opens the possibility of investigating not only the behaviour of electrons in a curved quasi-two-dimensional space, and the effects of varying that curvature, but also presents a novel way of investigating electron transport properties in a non-uniform transverse high magnetic field. It is shown that a semi-infinite two-dimensional electron gas subjected to a non-uniform magnetic field has, in addition to current-carrying edge states, one-dimensional states which lie within the interior of the gas, which also have a finite dispersion, an effect which may be used to create quantum wires or other structures. It is also shown that, in the absence of a magnetic field, curvature of the two-dimensional electron gas gives rise to a potential variation which is inversely proportional to the square of the radius of curvature, an effect which may also be used to confine the electronic motion to one dimension.