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\ntransition and one-dimensional (1D) Weyl nodes in the quantum limit of\nthree-dimensional pentatellurides, as they own low carrier densities and can\nachieve the extreme quantum limit at a low magnetic field. In this paper, we\nwill investigate the conditions for the existence of the 1D Weyl nodes and\ntheir dc transport properties. We find that in the strong topological insulator\n(TI) phase of ZrTe5, the formation of the Weyl nodes depends heavily on the\ncarrier density; while in the weak TI phase of HfTe5, the Weyl nodes are more\nlikely to appear. These behaviors are attributed to the fact that in the strong\nand weak TI phases, the zeroth Landau levels exhibit opposite evolutions with\nthe magnetic field. Moreover, the signatures of the critical fields that\ncharacterize the distinct behaviors of the system can be directly captured in\nthe conductivities.\n