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The Halperin $(m',m,n)$ fractional quantum Hall effects of two-componentquantum particles are studied in topological checkerboard lattice models. Herefor $m\neq m'$, we demonstrate the emergence of fractional quantum hall effectswith the associated $\mathbf{K}=\begin{pmatrix} m+2 & 1\\ 1 & m\\\end{pmatrix}$ matrix (even $m=2$ for boson and odd $m=3$ for fermion) in thepresence of both strong intercomponent and intracomponent repulsions. Throughexact diagonalization and density-matrix renormalization group calculations, weelucidate their topological fractionalizations, including (i) the$\det|\mathbf{K}|=(m^2+2m-1)$-fold ground-state degeneracies and (ii)fractionally quantized topological Chern number matrix$\mathbf{C}=\mathbf{K}^{-1}$. Our flat band model provides a paradigmaticexample of a microscopic Hamiltonian featuring fractional quantum Hall effectwith partial spin-polarization.

Halperin $(m',m,n)$ fractional quantum Hall effect in topological flat bands