Interband spectroscopy of Landau levels and magnetoexcitons in bulk black phosphorus

Low-dimensional systems based on black phosphorus (BP) have recently attracted much interest. Since the crystal structure of BP consists of 2D layers with a strong in-plane anisotropy, its electronic properties at a high magnetic field ($B$) are quite interesting. Here, we report a magneto-optical study of bulk BP at high $B$ to 12 T perpendicular to the 2D layers. In the obtained optical conductivity spectra, periodic peaks are clearly observed corresponding to Landau levels of up to $n$=6 quantum number. They exhibit almost linear shifts with $B$, and from their analysis an electron-hole reduced mass of 0.13 $m_0$ is obtained, where $m_0$ is the electron mass. Many of the peaks appear in pairs, which is interpreted in terms of Zeeman splitting and an electron-hole combined $g$-factor of 6.6 is obtained. In addition, magnetoexciton peaks are observed to shift quadratically with $B$, and the exciton binding energy at $B$=0 is estimated to be 9.7 meV.