Quantum Hall effect in topological Dirac semimetals modulated by the Lifshitz transition of the Fermi arc surface states

We investigate the magnetotransport of topological Dirac semimetals (DSMs) while taking into account the Lifshitz transition of the Fermi arc surface states. We demonstrate that a bulk momentum-dependent gap term, which is usually neglected in the study of bulk energy-band topology, can cause the Lifshitz transition by developing an additional Dirac cone on the surface to prevent the Fermi arcs from connecting with the bulk Dirac points. As a result, Weyl orbits can be turned off by the surface Dirac cone without destroying the bulk Dirac points. In response to the surface Lifshitz transition, the Weyl-orbit mechanism for the three-dimensional (3D) quantum Hall effect (QHE) in topological DSMs will break down. The resulting quantized Hall plateaus can be thickness dependent, similar to those based on Weyl orbits but their widths and quantized values become irregular. Accordingly, we propose that apart from bulk Weyl nodes and Fermi arcs, surface Lifshitz transitions are also crucial for realizing stable Weyl orbits and 3D QHE in real materials.