Anomalous Conductivity Tensor and Quantum Oscillations in the Dirac Semimetal Na$_{3}$Bi

Na$_{3}$Bi is a 3D Dirac semimetal with protected nodes. Angle-resolved photoemission experiments have observed these massless Dirac fermions in the bulk band, but transport experiments have been hampered by the extreme air sensitivity of Na$_{3}$Bi crystals. Transport experiments can potentially address interesting issues such as charge pumping between the separated Weyl nodes when the time-reversal symmetry is broken by a strong magnetic field. Here we report a transport measurement that reveals robust anomalies in both the conductivity and resistivity tensors. The resistivity $\rho_{xx}$ is B-linear up to 35 T, while the Hall angle exhibits an unusual profile approaching a step-function. In addition, we have also observed a prominent beating pattern in the Shubnikov de Haas (SdH) oscillations indicating the existence of two nearly equal SdH frequencies when the Fermi energy falls inside the non-trivial gap-inverted regime.