  We propose an innovative design for topological quantum batteries that
involves coupling two atoms to a one-dimensional lattice with topological
features. Employing the resolvent method, we analytically explore the
thermodynamic performances of quantum batteries (QBs). First, we demonstrate
that only coherent bound states significantly contribute to the stored energy
of QBs. We observe near-perfect energy transfer from the quantum charger to the
quantum battery (QB) in the topologically nontrivial phase. Conversely, in the
topologically trivial phase, we reveal that under the Markov limit, the
charging process of the QB is almost completely prohibited due to the emergence
of degenerate zero-energy bound states. Moreover, we discover that the maximum
energy storage exhibits singular behavior at the phase boundaries. Second, we
find that direct coupling between the QB and quantum charger renders the
ergotropy immune to sublattice dissipation, facilitated by the presence of a
dark state and vacancy-like dressed bound state. Further, we show that as
dissipation intensifies along with the emergence of the quantum Zeno effect,
the charging power of QBs is transiently enhanced. Our findings provide
insightful guidelines for practically enhancing the performance of QBs through
structured reservoir engineering.
