  In the search of fractional quantum anomalous Hall (FQAH) effects, the
conventional wisdom is to start from a flat Chern band isolated from the rest
of the Hilbert space by bandgap, so that many-body interaction can be projected
to a landscape that mimics a Landau level. Here we report the finding of FQAH
in a 2D semimetal. Described by a 2{\pi}-flux dice lattice, the model features
a flat band in touching with a dispersive lower band, where the band touching
is symmetry-protected from being gapped by electron interaction. At 1/3 and 2/3
filling of the gapless flat band, FQAH phases are found using density matrix
renormalisation group calculations taking into accounts all bands. Symmetry
breaking to gap the band touching can turn the semimetal into a Chern insulator
while keeping the Chern band nearly flat, but counter-intuitively this
suppresses the FQAH, as the gap opening introduces strong inhomogeneity to the
quantum geometry. We show an optical scheme to realize the 2{\pi}-flux dice
lattice for cold atoms. Our finding uncovers a new arena for the exploration of
fractional quantum Hall physics in addition to the Landau levels and Chern
insulators.
