Thin wire hall effect devices

A thin wire inside a bulk semiconductor can concentrate the current density and the magnetic field strength to intensities that are significant for the Hall effect. Also, the self-magnetic field of the Hall currents can add to this intensification, particularly when there is axial symmetry and a toroidal configuration. The impedanceZiacross the ends of the wire is modified if a currentIflows between the semiconductor and the wire:|Zi| \simeq \omega / \sigma . K_{H}. I[(b/a)^{k} -1]wherek = \micro .\sigma . K_{H}.I/(2.\pi)andaandbare the inner and outer radii of a cylinder. A more complete analysis of the cylindrical field problem reveals that well-known results for skin effect are also modified by the current. The new solution is expressed by high-order Thompson functions, which include the ber and bei functions of skin effect as a special case. For values ofkgreater than 2, the solution can have a negative real wave impedance. Experiments are described for estimating changes in the Hall currents by counting flux jumps in a superconducting wire which is embedded in bulk bismuth. The Hall currents are magnified by the factor 5. In the course of the experiments, a pulse position modulator is realized. Other possible devices are realizable, notably an amplifier and a simple, rugged flip-flop.