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

The ability to produce deliberately shaped or curved two-dimensional e lectron gases in semiconductors using recent developments in technolog y, for example regrowth of III-V semiconductors on patterned or etched substrates, opens the possibility of investigating not only the behav iour of electrons in a curved quasi-two-dimensional space, and the eff ects of varying that curvature, but also presents a novel way of inves tigating electron transport properties in a non-uniform transverse hig h magnetic field. It is shown that a semi-infinite two-dimensional ele ctron gas subjected to a non-uniform magnetic field has, in addition t o current-carrying edge states, one-dimensional states which lie withi n the interior of the gas, which also have a finite dispersion, an eff ect 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 t he two-dimensional electron gas gives rise to a potential variation wh ich 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.