Abstract
Since the Lorentz force is perpendicular to the magnetic field, it should not affect the motion of a charge along the field. This argument seems to imply absence of longitudinal magnetoresistance (LMR) which is, however, observed in many materials and reproduced by standard semiclassical transport theory applied to particular metals. We derive a necessary and sufficient condition on the shape of the Fermi surface for nonzero LMR. Although an anisotropic spectrum is a prerequisite for LMR, not all types of anisotropy can give rise to the effect: a spectrum should not be separable in any sense. More precisely, the combination , where is the radial component of the momentum in a cylindrical system with the axis along the magnetic field and is the radial (tangential) component of the velocity, should depend on the momentum along the field. For some lattice types, this condition is satisfied already at the level of nearest-neighbor hopping; for others, the required non-separabality occurs only if next-to-nearest-neighbor hopping is taken into account.
- Received 24 March 2010
DOI:https://doi.org/10.1103/PhysRevB.81.214438
©2010 American Physical Society
Synopsis
What would Lorentz say?
Published 28 June 2010
The shape of the Fermi surface in a material can explain the counterintuitive effect of longitudinal magnetoresistance
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