Anisotropic magnetoresistance is the change tendency of resistance of a material on the mutual orientation of the electric current and the external magnetic field. Here, we report experimental observations in the Dirac semimetal ${\mathrm{Cd}}_3{\mathrm{As}}_2$ of giant anisotropic magnetoresistance and its transverse version, called the planar Hall effect. The relative anisotropic magnetoresistance is negative and up to −68% at 2 K and 10 T. The high anisotropy and the minus sign in this isotropic and nonmagnetic material are attributed to a field-dependent current along the magnetic field, which may be induced by the Berry curvature of the band structure. This observation not only reveals unusual physical phenomena in Weyl and Dirac semimetals, but also finds additional transport signatures of Weyl and Dirac fermions other than negative magnetoresistance.

• Received 9 March 2018
• Revised 30 April 2018

DOI:https://doi.org/10.1103/PhysRevB.97.201110