TITLE:
The Classical Hall Effect in Multiply-Connected Plane Regions Part II: Spiral Current Streamlines
AUTHORS:
Udo Ausserlechner
KEYWORDS:
Circulating Current, Corbino Disk, Corbino Images, Corbinotron, Doubly Connected, Hall Plate, Loop Current, Multiply Connected, Non-Peripheral Contacts, Reverse Magnetic Field Reciprocity, Spiral Streamlines, Stream Function
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.10,
October
11,
2019
ABSTRACT: Multiply-connected Hall plates show different phenomena than singly connected Hall plates. In part I (published in Journal of Applied Physics and Mathematics), we discussed topologies where a stream function can be defined, with special reference to Hall/Anti-Hall bar configurations. In part II, we focus on topologies where no conventional stream function can be defined, like Corbino disks. If current is injected and extracted at different boundaries of a multiply-connected conductive region, the current density shows spiral streamlines at strong magnetic field. Spiral streamlines also appear in simply-connected Hall plates when current contacts are located in their interior instead of their boundary, particularly if the contacts are very small. Spiral streamlines and circulating current are studied for two complementary planar device geometries: either all boundaries are conducting or all boundaries are insulating. The latter case means point current contacts and it can be treated similarly to singly connected Hall plates with peripheral contacts through the definition of a so-called loop stream function. This function also establishes a relation between Hall plates with complementary boundary conditions. The theory is explained by examples.