A positive active material for a rechargeable lithium battery includes a lithium nickel-based composite oxide including a secondary particle in which a plurality of plate-shaped primary particles are agglomerated; and a lithium manganese composite oxide having at least two crystal lattice structures, wherein the secondary particle has a regular array structure in which (003) planes of the primary particles are oriented in a vertical direction with respect to the surface of the secondary particle.

A mixed conductor represented by Formula 1:
A.sub.4±xTi.sub.5−yG.sub.zO.sub.12−δ  Formula 1 wherein, in Formula 1, A is a monovalent cation, G is at least one of a monovalent cation, a divalent cation, a trivalent cation, a tetravalent cation, a pentavalent cation, or a hexavalent cation, with the proviso that G is not Ti or Cr, wherein 0<x<2, 0.3<y<5, 0<z<5, and 0<δ≤3.

A mixed conductor represented by Formula 1:
A.sub.4+xM.sub.5-yM′.sub.yO.sub.12-δ,  Formula 1
wherein, in Formula 1, A is a monovalent cation, M is at least one of a divalent cation, a trivalent cation, or a tetravalent cation, M′ is at least one of a monovalent cation, a divalent cation, a trivalent cation, a tetravalent cation, a pentavalent cation, or a hexavalent cation, M and M′ are different from each other, and 0.3≤x<3, 0.01<y<2, and 0≤δ≤1 are satisfied.

A positive active material for a rechargeable lithium battery includes a lithium nickel-based composite oxide including a secondary particle in which a plurality of plate-shaped primary particles are agglomerated; and a lithium manganese composite oxide having at least two crystal lattice structures, wherein the secondary particle has a regular array structure in which (003) planes of the primary particles are oriented in a vertical direction with respect to the surface of the secondary particle.

A mixed conductor represented by Formula 1:

A.sub.4+xM.sub.5-yM.sub.yO.sub.12-,Formula 1

wherein, in Formula 1, A is a monovalent cation, M is at least one of a divalent cation, a trivalent cation, or a tetravalent cation, M is at least one of a monovalent cation, a divalent cation, a trivalent cation, a tetravalent cation, a pentavalent cation, or a hexavalent cation, M and M are different from each other, and 0.3x<3, 0.01<y<2, and 01 are satisfied.

A mixed conductor represented by Formula 1:

A.sub.xTi.sub.5yG.sub.zO.sub.12Formula 1 wherein, in Formula 1, A is a monovalent cation, G is at least one of a monovalent cation, a divalent cation, a trivalent cation, a tetravalent cation, a pentavalent cation, or a hexavalent cation, with the proviso that G is not Ti or Cr, wherein 0<x<2, 0.3<y<5, 0<z<5, and 0<3.

Disclosed are a grain boundary- and surface-doped lithium-lanthanum-zirconium composite oxide solid electrolyte, a preparation method therefor, and an application thereof. Part of doping elements are step-doped at the grain boundary and the surface of the lithium-lanthanum-zirconium composite oxide solid electrolyte to improve the distribution state of the doping elements at the grain boundaries, reduce the number of grain boundaries, lower the grain boundary resistance of the lithium-lanthanum-zirconium composite oxide, thereby obtaining high ionic conductivity. The doping method has the advantages of being simple and convenient in process, low in cost and high in universality, can meet the requirements of different solid electrolytes on doping elements, and is suitable for large-scale application. The solid electrolyte obtained from the technical solution of the present application can be used in fields such as all-solid-state lithium or lithium ion batteries, semi-solid lithium ion batteries, lithium air batteries and the like.