  The Dirac material ZrTe$_5$ at very low carrier density was recently found to
be a nodal-line semimetal, where ultra-flat bands are expected to emerge in
magnetic fields parallel to the nodal-line plane. Here we report that in very
low carrier-density samples of ZrTe$_5$, when the current and the magnetic
field are both along the crystallographic $a$ axis, the current-voltage
characteristics presents a pronounced nonlinearity which tends to saturate in
the ultra quantum limit. The magnetic-field dependence of the nonlinear
coefficient is well explained by the Boltzmann theory for flat-band transport,
and we argue that this nonlinear transport is likely due to the combined effect
of flat bands and charge puddles, the latter appear due to very low carrier
densities.
