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We study the quantum Hall effect of 2D electron gas in black phosphorus inthe presence of perpendicular electric and magnetic fields. In the absence of abias voltage, the external magnetic field leads to a quantization of the energyspectrum into equidistant Landau levels, with different cyclotron frequenciesfor the electron and hole bands. The applied voltage reduces the band gap, andeventually a semiconductor to semimetal transition takes place. This nontrivialphase is characterized by the emergence of a pair of Dirac points in thespectrum. As a consequence, the Landau levels are not equidistant anymore, butfollow the $\varepsilon_n\propto \sqrt{nB}$ characteristic of Dirac crystals asgraphene. By using the Kubo-Bastin formula in the context of the kernelpolynomial method, we compute the Hall conductivity of the system. We obtain a$\sigma_{xy}\propto 2n$ quantization of the Hall conductivity in the gappedphase (standard quantum Hall effect regime), and a $\sigma_{xy}\propto4(n+1/2)$ quantization in the semimetalic phase, characteristic of Diracsystems with non-trivial topology.

Quantum Hall effect and semiconductor to semimetal transition in biased black phosphorus