Quantum magnetoresistance of Weyl semimetals with strong Coulomb disorder

Abstract

We study the effects of strong Coulomb disorder on the transverse magnetoresistance in Weyl semimetals at low temperatures. Using the diagrammatic technique and the Keldysh model to sum up the leading terms in the diagrammatic expansion, we find that the linear magnetoresistance exhibits a strong renormalization due to the long-range nature of the Coulomb interaction ${\ensuremath{\rho}}_{xx}\ensuremath{\propto}H\phantom{\rule{0.16em}{0ex}}ln(eH\ensuremath{\hbar}{v}^{2}/c{T}_{\mathrm{imp}}^{2}),\phantom{\rule{4pt}{0ex}}\mathrm{\ensuremath{\Omega}}{\ensuremath{\alpha}}^{\ensuremath{-}1/6}\ensuremath{\ll}{T}_{\mathrm{imp}}\ensuremath{\ll}\mathrm{\ensuremath{\Omega}}/{\ensuremath{\alpha}}^{\ensuremath{-}3/4}$, where $\mathrm{\ensuremath{\Omega}}=v\sqrt{2eH\ensuremath{\hbar}/c}$ is the distance between the zeroth and the first Landau levels, ${T}_{\mathrm{imp}}=\ensuremath{\hbar}v{n}_{\mathrm{imp}}^{1/3}$ measures the strength of the impurity potential in terms of the impurity concentration $n$ and the Fermi velocity $v$, and $\ensuremath{\alpha}={e}^{2}/\ensuremath{\hbar}v$ is the effective fine structure constant of the material. As disorder becomes even stronger (but still in the parametric range, where the Coulomb interaction can be treated as a long-range one), we find that the magnetoresistivity becomes quadratic in the magnetic field ${\ensuremath{\rho}}_{xx}\ensuremath{\propto}{H}^{2}$.