Lithium-rich manganese-based positive electrode active material and battery

The invention provides a lithium-rich manganese-based positive electrode active material and a battery. The invention provides a lithium-rich manganese-based positive electrode active material on the first aspect, the lithium-rich manganese-based positive electrode active material comprises matrix particles and a coating layer coating the outer surfaces of the matrix particles, the molecular formula of the matrix particles is Lia-b1Kc-b2MnxCoyNizMhO2-dDd, and the matrix particles have lithium vacancies and potassium vacancies. According to the lithium-rich manganese-based positive electrode active material provided by the invention, the potassium element occupies part of lithium sites, so that the use amount of a lithium source is reduced, the rate capability and the structural stability of the material are improved, and meanwhile, the formation of the potassium vacancies is beneficial to accommodating lithium ions embedded back in the discharge process, so that the specific discharge capacity and the first c