Magnetotransport in Dirac metals: Chiral magnetic effect and quantum oscillations

Dirac metals are characterized by the linear dispersion of fermionic quasiparticles, with the Dirac point hidden inside a Fermi surface. We study the magnetotransport in these materials using chiral kinetic theory to describe within the same framework both the negative magnetoresistance caused by the chiral magnetic effect and quantum oscillations in the magnetoresistance due to the existence of the Fermi surface. We discuss the relevance of obtained results to recent measurements on ${\mathrm{Cd}}_3{\mathrm{As}}_2$.

Figure 1

The semiclassical picture of the Fermi surface for right and left chiral modes is shown in the presence of the magnetic field. For the linear dispersion, the support of Hamiltonian eigenstates is a collection of cylinders corresponding to eigenvalues ${\varepsilon }_n\left(k_z\right)=\hslash v_F\sqrt{k_z^2+k_{\perp }^2}$, where $k_{\perp }^2=2eBn$ with $n=0,1,2,...$ . The state with $n=0$ is chiral and exists only for $p_z>0$ (parallel to $B)$ for the right chirality and for $p_z<0$ for the left one.

Figure 2

Longitudinal magnetoresistance as a function of the magnetic field. We used numerical values consistent with [17] $k_F=3.8\times {10}^8{\text{m}}^{-1},v_F=9.3\times {10}^5\mathrm{m}/\mathrm{s},\tau =8\times {10}^{-13}\text{s}$, and $T=2.5\text{K}$. The plots are made for three values of ${\tau }_Q/\tau =0$, 1, and 16 and for ${\tau }_v=10\tau$.