Combining various two-dimensional materials into novel van der Waals (vdW) heterostructures has been shown to lead to new emergent quantum systems. A novel heterostructure composed of a vdW topological insulator (TI) such as Bi$_{2}$Se$_{3}$ with a quantum spin liquid (QSL) such as $alpha$-RuCl$_{3}$ is of great interest for the potential for the chiral Dirac electrons in the TI surface states to interact strongly with the fractionalized fermionic spin excitations in the QSL. We report the heteroepitaxial growth of Bi$_{2}$Se$_{3}$ thin films on $alpha$-RuCl$_{3}$ as well as the characterization of their structural and electrical properties. Bi$_{2}$Se$_{3}$ thin films with an atomically smooth and uniform surface are grown by molecular beam epitaxy. The heterostructure exhibits a preferential epitaxial relationship corresponding to $(5 times 5)-$Bi$_{2}$Se$_{3}/(2sqrt{3} times 2sqrt{3})R30deg-alpha$-RuCl$_{3}$ commensurate supercells with a periodicity of 1.2 nm. The formation of the superlattice despite a lattice mismatch as large as 60% is attributed to the van der Waals heteroepitaxy. Magnetotransport measurements as a function of temperature show Bi$_{2}$Se$_{3}$ films grown on $alpha$-RuCl$_{3}$ are heavily $n$-doped, $n_{e}$ ~10$^{14}$ cm$^{-2}$, with mobility $mu$ ~450 cm$^{2}$ V$^{-1}$ s$^{-1}$ at low temperatures.
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