Linear geometrical magnetoresistance effect: Influence of geometry and material composition

This work reports theorems on geometrical magnetoresistance effects in simply or multiply connected surfaces. We consider planar or three-dimensional device geometries, and assume that the current/voltage relations are linear. It is shown that the resistance of any two-wire device must be an even function of the magnetic field. We further calculate the magnitude of the highest and lowest second-order geometrical magnetoresistance of a planar two-wire device, for given isotropic material parameters. The largest change in magnetoresistance occurs when the boundaries of the device contain only electrically conducting leads and no insulating components. When the Fermi surface and the mobility tensor are isotropic, as is the case for n-type InAs and InSb, the magnetoresistance obtained in the Corbino geometry is the largest possible, but this conclusion does not generalize to materials with anisotropic conductivity tensors. The presence of multiple ellipsoidal carrier pockets in Bi also explains why the geometrical magnetoresistance effects are much smaller in the trigonal plane of Bi than in InAs, even though these materials have similar mobilities at room temperature, and the conductivity of Bi is isotropic in that plane.