  The quantum limit can be easily reached in the Dirac semimetals under the
magnetic field, which will lead to some exotic many-body physics due to the
high degeneracy of the topological zeroth Landau bands (LBs). By solving the
effective Hamiltonian, which is derived by tracing out the high energy degrees
of freedom, at the self-consistent mean field level, we have systematically
studied the instability of Dirac semimetal under a strong magnetic field. A
charge density wave (CDW) phase and a polarized nematic phase formed by
"exciton condensation" are predicted as the ground state for the tilted and
untilted bands, respectively. Furthermore, we propose that, distinguished from
the CDW phase, the polarized nematic phase can be identified in experiments by
anisotropic transport and Raman scattering.
