Unconventional ferromagnetism and superconductivity in the imbalanced
kagome-lattice Hubbard model are investigated by the mean-field theory and
determinant quantum Monte Carlo method. Due to the asymmetric band structure of
kagome lattice, the spin-z ferromagnetic order intrinsically exists in the
system, which is first enhanced by the interaction, and then continuously
destructed after reaching a maximum at a moderate interaction strength. In
contrast, the xy-plane ferromagnetism develops only above a critical
interaction, which is estimated to be Uc​/t=3.65±0.05 by finite-size
scaling. We further verify the nature of the above transverse magnetic
transition, and demonstrate it belongs to the three-dimensional XY
universality class. Finally, we study the superconducting property, and reveal
the possible superconducting state has a triplet f-wave pairing symmetry. Our
results uncover the exotic quantum states induced by the interactions on kagome
lattice, and provide important insights regarding the interplay between
electronic correlations and geometry frustrations