Second-order topological insulator under strong magnetic field

We study a three-dimensional chiral second-order topological insulator (SOTI) subject to a magnetic field. Via its gauge field, the applied magnetic field influences the electronic motion on the lattice, and via the Zeeman effect, the field influences the electronic spin. We compare an effective surface theory to a full lattice model of the SOTI. Without magnetic field, the surface theory shows good agreement with our lattice calculations, accurately predicting the surface gap as well as the spin and orbital components of the states at the edges of the surface Dirac bands. However, when a gauge field is applied, the Landau level spectrum obtained from the lattice theory deviates from that predicted by the surface theory. On any given surface, the lowest Landau level is found closer to zero energy than is predicted by the surface theory. Further, while the first excited levels approximately match their predicted spatial, spin, and (on-site) orbital dependence, these levels are missing their expected opposite-energy partners.

Ref: B. A. Levitan and T. Pereg-Barnea, Phys. Rev. Research 2, 033327 (2020)