  Recent spatially resolved observations of galaxies at z=0.6-3 reveal that
high-redshift galaxies show complex kinematics and a broad distribution of
gas-phase metallicity gradients. To understand these results, we use a suite of
high-resolution cosmological zoom-in simulations from the Feedback in Realistic
Environments (FIRE) project, which include physically motivated models of the
multi-phase ISM, star formation, and stellar feedback. Our simulations
reproduce the observed diversity of kinematic properties and metallicity
gradients, broadly consistent with observations at z=0-3. Strong negative
metallicity gradients only appear in galaxies with a rotating disk, but not all
rotationally supported galaxies have significant gradients. Strongly perturbed
galaxies with little rotation always have flat gradients. The kinematic
properties and metallicity gradient of a high-redshift galaxy can vary
significantly on short time-scales, associated with starburst episodes.
Feedback from a starburst can destroy the gas disk, drive strong outflows, and
flatten a pre-existing negative metallicity gradient. The time variability of a
single galaxy is statistically similar to the entire simulated sample,
indicating that the observed metallicity gradients in high-redshift galaxies
reflect the instantaneous state of the galaxy rather than the accretion and
growth history on cosmological time-scales. We find weak dependence of
metallicity gradient on stellar mass and specific star formation rate (sSFR).
Low-mass galaxies and galaxies with high sSFR tend to have flat gradients,
likely due to the fact that feedback is more efficient in these galaxies. We
argue that it is important to resolve feedback on small scales in order to
produce the diverse metallicity gradients observed.
