  Metal-insulator transitions driven by magnetic fields have been extensively
studied in 2D, but a 3D theory is still lacking. Motivated by recent
experiments, we develop a scaling theory for the metal-insulator transitions in
the strong-magnetic-field quantum limit of a 3D system. By using a
renormalization-group calculation to treat electron-electron interactions,
electron-phonon interactions, and disorder on the same footing, we obtain the
critical exponent that characterizes the scaling relations of the resistivity
to temperature and magnetic field. By comparing the critical exponent with
those in a recent experiment [Tang et al., Nature 569, 537 (2019)], we conclude
that in which the insulating ground state was not only a charge density wave
driven by electron-phonon interactions but also coexisting with strong
electron-electron interactions and back-scattering disorder. Our theory will be
helpful for exploring the emergent territory of 3D metal-insulator transitions
under strong magnetic fields.
