Quantum Hall effect in Dirac semimetal films

To understand quantum Hall effects in films of 3D Dirac semimetals observed in recent experiments, we studied the contributions of various topological boundary states contributions. We found that there can be a Lifshitz-like transition with reconnection of surface Fermi arcs. Particularly, as the chemical potential varies, open Fermi arcs may loop around with its two ends connecting the same surface projected Dirac point. This allows a doubled frequency in the quantum oscillations via Möbius Weyl orbits as the electron loops twice at the top and bottom surfaces respectively and tunnels through the bulk at the Dirac point in between, which traces the boundary of a Möbius strip. In addition, we also discussed the interplay between the contributions from the edge states and bulk sub-bands to the quantum Hall effect.