Magneto-transport at high Hall angles: a comparison of the high-magnetic-field and high-mobility (quantum Hall effect) limits in the Hall bar and Corbino disc configurations

Abstract

Examines the Hall angle ( theta ) dependence of geometrical magnetoresistance, with emphasis on the theta to 90 degrees limit. A comparison of the four cases mentioned in the title benefits from the use of alternative notations for the two kinds of limits, and from the basic idea that the Corbino disc (CD) and the Hall bar (HB) have two and one theta -dependent effective dimensions, respectively. One of these dependences is cancelled under QHE conditions, relative to the behaviour in the traditional high-magnetic-field limit. As theta to 90 degrees , this produces no qualitative changes in the CD, but a fundamental difference, with useful experimental consequences, in the HB. The alternative notation also provides a clear explanation for some unusual characteristics of the CD under QHE conditions, namely a finite current density with zero current, and a zero resistivity with infinite resistance. The paper also includes some clarifying remarks on the relationships between the conductivity and resistivity tensors in the two kinds of limits, and on the classical and quantum-mechanical origins of a number of phenomena which ultimately make it possible to achieve highly accurate QHE measurements.