**6. Electric properties of cuprate**

Undoped Ln2CuO4 cuprates are weak electrical conductors [53] because they have neither free electrons nor anionic vacancy. This low conductivity is due to the presence of two oxidation states of copper Cu2+ and Cu+ . However, doping gives rise to defects or free electrons which allow electrical conduction.

An electrical conductor allows the passage of electrical current and indicates that in this solid, there are structural defects and/or conduction electrons. For La2–x(Ba,Sr) xCuO4±δ, each electron with a valence of 6s of Ba or 5s of Sr interacts with 2p of oxygen [54]. This interaction corresponds to the energy that participates in the formation of the solid. This energy associated with the interaction stabilizes the valence electron and prevents it from participating in electrical conductivity, which makes the material insulating. It is, therefore, necessary for the valence electrons to be able to participate in electrical conductivity so that they are freed from their bond of valence.

When the electrical current is established, a part of the electrical energy is still distributed over all the ordered atoms, barely modifying the different movements of the electrons, which can no longer leave their atom except in the absence of a defect. On the other hand, for atoms in a defect position, their conduction electron no longer has a synchronous movement with the others, and they can more easily receive electrical energy. As a result, when the electrical current is established, the conduction electrons of the atoms in the defect position can gradually leave their atom, which allows the disturbances generated by the connections to propagate [55]. It is the electrical energy that allows them to cross the gap, which without it, it retains in their corresponding atom. It is appropriate to call such defects with conductors to distinguish them from other resistant structural defects. This is a situation reminiscent of the semiconductor state, the difference coming from the number of defects, and more numerous carriers in a metal or a metallic oxide. Metal is a conductor in which conduction electrons are excited by energy electric.

The mechanism of conductivity in cuprates considers the conductive solid as a mixture of two phases: one ordered and the other disordered. If in the disordered phase, there are too many resisting defects close to the paths of the electrons, then the body is conductive, semi-conductive, or insulating at any temperature [56]. If the number of resistant defects is sufficiently low, the body is superconducting. The notion of resistant defects has the advantage of making it possible to understand the significant difference between oxides and metals. The 2p holes on the oxygen atoms are resistant defects. Due to the importance of electrical properties for this family of materials, they are used in several areas of electricity and energy storage such as solid-oxide fuel cells and capacitors. Indeed, cuprates are used as cathodes for fuel cells. These cathodes must be good electrical and ionic conductors, stable in an oxidizing medium, and compatible with the electrolyte and interconnector materials. The most encountered materials are of the A1−xSrxBO3 type, such as manganite and lanthanum cobaltite doped with strontium La0.6Sr0.4MnO3 (LSM) [57] and La0.7Sr0.3CoO3−δ (LSC) [58]. Recently, new materials of general formula A2MO4+δ with RP structure have been studied and show promising results.
