  We study the quantum Hall effect of 2D electron gas in black phosphorus in
the presence of perpendicular electric and magnetic fields. In the absence of a
bias voltage, the external magnetic field leads to a quantization of the energy
spectrum into equidistant Landau levels, with different cyclotron frequencies
for the electron and hole bands. The applied voltage reduces the band gap, and
eventually a semiconductor to semimetal transition takes place. This nontrivial
phase is characterized by the emergence of a pair of Dirac points in the
spectrum. As a consequence, the Landau levels are not equidistant anymore, but
follow the $\varepsilon_n\propto \sqrt{nB}$ characteristic of Dirac crystals as
graphene. By using the Kubo-Bastin formula in the context of the kernel
polynomial method, we compute the Hall conductivity of the system. We obtain a
$\sigma_{xy}\propto 2n$ quantization of the Hall conductivity in the gapped
phase (standard quantum Hall effect regime), and a $\sigma_{xy}\propto
4(n+1/2)$ quantization in the semimetalic phase, characteristic of Dirac
systems with non-trivial topology.
