  In this paper we have systematically studied the electronic instability of
pressured black phosphorous (BP) under strong magnetic field. We first present
an effective model Hamiltonian for pressured BP near the Lifshitz point. We
show that when the magnetic field exceeds a certain critical value, the
nodal-line semimetal (NLSM) state of BP with a small band overlap re-enters
semiconductive phase by re-opening a small gap. This results in a narrow-band
semiconductor with a partially flat valence band edge. We show that above this
critical magnetic field, two possible instabilities, i.e., charge density wave
(CDW) phase or excitonic insulator (EI) phase, are predicted as the ground
state for high and low doping concentrations, respectively. By comparing our
results with the experiment, we suggest the field-induced instability observed
in recent experiment as EI. Furthermore, we propose that the semimetallic BP
under pressure with small band overlaps may provide a good platform to study
the magneto-exciton insulators. Our findings bring the first insight into the
electronic instability of topological NLSM in the quantum limit.
