Magnetic field driven Lifshitz transition and one-dimensional Weyl nodes in three-dimensional pentatellurides

Recent experiments reported that the magnetic field can drive the Lifshitz transition and one-dimensional (1D) Weyl nodes in the quantum limit of three-dimensional pentatellurides, as they own low carrier densities and can achieve the extreme quantum limit at a low magnetic field. In this paper, we will investigate the conditions for the existence of the 1D Weyl nodes and their dc transport properties. We find that in the strong topological insulator (TI) phase of ZrTe5, the formation of the Weyl nodes depends heavily on the carrier density; while in the weak TI phase of HfTe5, the Weyl nodes are more likely to appear. These behaviors are attributed to the fact that in the strong and weak TI phases, the zeroth Landau levels exhibit opposite evolutions with the magnetic field. Moreover, the signatures of the critical fields that characterize the distinct behaviors of the system can be directly captured in the conductivities.