  Multicomponent quantum Hall effect, under the interplay between
intercomponent and intracomponent correlations, leads us to new emergent
topological orders. Here, we report the theoretical discovery of fractional
quantum hall effect of strongly correlated Bose-Fermi mixtures classified by
the $\mathbf{K}=\begin{pmatrix} m & 1\\ 1 & n\\ \end{pmatrix}$ matrix (even $m$
for boson and odd $n$ for fermion), using topological flat band models.
Utilizing the state-of-the-art exact diagonalization and density-matrix
renormalization group methods, we build up the topological characterization
based on three inherent aspects: (i) topological $(mn-1)$-fold ground-state
degeneracy equivalent to the determinant of the $\mathbf{K}$ matrix, (ii)
fractionally quantized topological Chern number matrix equivalent to the
inverse of the $\mathbf{K}$ matrix, and (iii) two parallel-propagating chiral
edge branches with level counting $1,2,5,10$ consistent with the conformal
field theory description.
