  We study the effect of strong magnetic field on competing chiral and diquark
order parameters in a regime of moderately dense quark matter. The
inter-dependence of the chiral and diquark condensates through nonperturbative
quark mass and strong coupling effects is analyzed in a two-flavor
Nambu-Jona-Lasinio (NJL) model. In the weak magnetic field limit, our results
agree qualitatively with earlier zero-field studies in the literature that find
a critical coupling ratio $G_D/G_S\sim 1.1$ below which chiral or
superconducting order parameters appear almost exclusively. Above the critical
ratio, there exists a significant mixed broken phase region where both gaps are
non-zero. However, a strong magnetic field $B\gtrsim 10^{18}$ G disrupts this
mixed broken phase region and changes a smooth crossover found in the
weak-field case to a first-order transition for both gaps at almost the same
critical density. Our results suggest that in the two-flavor approximation to
moderately dense quark matter, strong magnetic field enhances the possibility
of a mixed phase at high density, with implications for the structure,
energetics and vibrational spectrum of neutron stars.
