LAUSR

We examine instabilities of the plateau phases in the spin-$\frac{1}{2}$ kagome lattice antiferromagnet in an applied field by means of degenerate perturbation theory, and find some emergent supersolid phases below the $m=\frac{5}{9}$ plateau. The wave functions of the plateau phases in a magnetic field have the particular construction based on the building blocks of resonating hexagons and their surrounding sites. Magnon excitations on each of these blocks suffer from a kinetic frustration effect, namely, they cannot hop easily to the others since the hopping amplitudes through the two paths destructively cancel out with each other. The itinerancy is thus weakened, and the system is driven toward the strong coupling regime, which together with the selected paths allowed in real space bears a supersolid phase. This mechanism is contrary to that proposed in lattice Bose gases, where the strong competing interactions suppress with each other, allowing a small kinetic energy scale to attain the itinerancy. Eventually, we find a supersolid state in which the pattern of resonating hexagons is preserved from the plateau crystal state and only one third of the originally polarized spins outside the hexagons dominantly join the superfluid component, or equivalently, participate in the magnetization process.