Linear magnetoresistance in metals: Guiding center diffusion in a smooth random potential

Abstract

We predict that guiding center (GC) diffusion yields a linear and nonsaturating (transverse) magnetoresistance in 3D metals. Our theory is semiclassical and applies in the regime where the transport time is much greater than the cyclotron period and for weak disorder potentials which are slowly varying on a length scale much greater than the cyclotron radius. Under these conditions, orbits with small momenta along magnetic field B are squeezed and dominate the transverse conductivity. When disorder potentials are stronger than the Debye frequency, linear magnetoresistance is predicted to survive up to room temperature and beyond. We argue that magnetoresistance from GC diffusion explains the recently observed giant linear magnetoresistance in 3D Dirac materials.

Transversal magnetotransport in Weyl semimetals: Exact numerical approach

“…Both modifications are relevant for experiments. Further, in the semiclassical limit, Song et al 42 proposed a guiding center picture of linear magnetoresistance that could be checked with our exact and fully quantum-mechanical approach.…”

Magnetoconductivity in Weyl semimetals: Effect of chemical potential and temperature

“…A quantum approach is necessary in order to understand the almost linear magnetoresistance associated with quantum oscillations observed in the experiments. Given the success of the semiclassical picture of guiding center motion in describing linear magnetoresistance in a Weyl semimetal [29], it will be very interesting to see whether it can be extended to a quantum version so that we can better understand the associated quantum oscillations. …”

“…[28] showed that a Coulomb impurity is crucial for the linear magnetoresistance found by Abrikosov. Meanwhile, Song et al [29] approached the problem from the point of view of the classical motion of a guiding center in the case of a random potential that is slowly varying in space. In the case in which the cyclotron orbit size is smaller than the distance scale of the variation of the random potential, they showed that linear magnetoresistance is obtained even when the chemical potential is far away from the Dirac neutrality point.…”

Magnetoresistance of semimetals: The case of antimony

“…The field-induced reduction in mobility can be caused by a disorder invisible to long-wavelength electrons at zerofield and becoming relevant in presence of magnetic field. Since the electron wave-function is smoothly squeezed by magnetic field, Raleigh scattering by extended defects becomes more efficient as the Landau levels are depopulated [21]. This provides a simple, but non-universal foundation for the field-induced decrease in mobility leading to the ubiquitous non-quadratic magnetoresistance.…”