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

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.

Figure 1

(a) Magnetoresistance can be dominated by guiding center (GC) motion when disorder correlation lengths $\xi \gg r_c$. Here $r_c$ is the cyclotron radius. This regime is characterized by slow GC motion, ${\mathbf{v}}_{\mathrm{gc}}={\nabla }_{\mathbf{r}}V\left(\mathbf{r}\right)\times \widehat{\mathbf{z}}/B$, accompanied by fast cyclotron orbits, ${\mathbf{v}}_{\mathrm{cycl}}$. GC diffusion in this environment givers rise to LMR. (b) Electrons perform closed orbits of the Fermi surface, with GC motion classified into two types, $k_z<k_z^{*}$ (red) and $k_z>k_z^{*}$ (blue); critical $k_z^{*}$ (green). (c) For $k_z<k_z^{*}$, electrons are squeezed in $z$ yielding mean free paths $\ell \approx \xi$ and in-plane $D_{xx}\sim v_{\mathrm{gc}}\xi \propto 1/B$. (d) In contrast, $k_z>k_z^{*}$ electrons exhibit unconstrained $z$ motion yielding in-plane $D_{xx}\sim v_{\mathrm{gc}}^2\xi /v_z\propto 1/B^2$ (see text).