We present a comprehensive theoretical study of the topological properties of triplon excitations in spin-$1/2$ dimer-singlet ground states defined on the maple-leaf and star lattices. Our analysis is based on a model that includes Heisenberg interactions, Dzyaloshinskii-Moriya (DM) interactions, and an external magnetic field. In the absence of an in-plane DM vector, we demonstrate that the triplon Hamiltonian maps onto the magnon Hamiltonian of the kagome lattice, inheriting its nontrivial topological characteristics, including Berry curvature and topological invariants such as the ${\mathbb{Z}}_2$ invariant and Chern numbers. This correspondence enables us to derive approximate analytical expressions for the spin Nernst and thermal Hall conductivities. Furthermore, we explore the effects of realistic finite in-plane DM interactions, uncovering multiple topological transitions and a complex thermal Hall conductivity behavior, including potential sign reversals as functions of magnetic field and temperature. Using layer groups, we also provide a symmetry classification of the star and maple-leaf lattices.

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• Magnetism
• Thermal Hall effect
• Triplon
• Quantum spin models
• Topological materials