π Oscillation phase shift between transverse and longitudinal magnetoconductivities in Weyl semimetals

Abstract

In the presence of a magnetic field $\mathbf{B}$, the negative transverse magnetoconductivity (TMC) for $\mathbf{E}\ensuremath{\perp}\mathbf{B}$, with $\mathbf{E}$ being the applied electric field, and anomalous positive longitudinal magnetoconductivity (LMC) for $\mathbf{E}\ensuremath{\parallel}\mathbf{B}$ of a three-dimensional (3D) Weyl semimetal (WSM) both exhibit periodic-in-$1/B$ quantum oscillations. We develop a semiclassical theory of the magnetoconductivities of a 3D WSM, taking into account the effect of the Landau level broadening and finite temperatures. We find that if one fixes the direction of $\mathbf{B}$ and switches the direction of $\mathbf{E}$ to be perpendicular and parallel to $\mathbf{B}$, there exists an interesting peak-valley correspondence, or, say, a relative $\ensuremath{\pi}$ oscillation phase shift, between the oscillating TMC and LMC. This can serve as unambiguous measurable evidence manifesting the distinct underlying physical mechanisms of the TMC and LMC in WSMs, which has so far not been reported in theories or experiments.