Energy spectrum of pristine and compressed black phosphorus in the presence of a magnetic field

The electronic properties of pristine and compressed bulk black phosphorus (BP) in the presence of a magnetic field perpendicular to a BP monolayer are investigated by using the tight-binding Hamiltonian model. Similar to that of graphite, the magnetic field can induce the flat, partially flat, and oscillatory Landau levels (LLs) in both kinds of BP, although there exist many distinct properties different from graphite, such as the oscillatory LL positions and the LL spacings. Also, the LLs exhibit richer dependences on the LL index, including a quadratic (linear) function of the LL index for the small (big) LL index. Furthermore, the topological node-line semimetal state in compressed BP caused by the strain is found to be sensitive to the magnetic field, indicating that even a very weak magnetic field is enough to break the node-line state. Meanwhile, it is shown that the strain can almost uniformly increase the LL spacing for the conductance band, while a different and complex LL spacing variation is observed for the valence band.