  We use the mean-field theory to analyze the ground-state phase diagrams of
spin-orbit coupled mass-imbalanced Fermi gases throughout the BCS-BEC
evolution, including both the population-balanced and -imbalanced systems. Our
calculations show that the competition between the mass and population
imbalance and the Rashba-type spin-orbit coupling (SOC) gives rise to very rich
phase diagrams, involving normal, superfluid and phase separated regions. In
addition, we find quantum phase transitions between the topologically trivial
gapped superfluid and the nontrivial gapless superfluid phases, opening the way
for the experimental observation of exotic phenomena with cold atom systems.
