Enlightening of the low-dimensional high-<italic>T</italic><sub>C</sub> superconductivity: Bond contraction and electron dual polarization

Abstract

<p indent=0mm>Electron-phonon interaction that couples the carriers for the Bose-Einstein condensation and the nature and configuration of the O−Cu chains and O−Cu planes that accommodate carriers are key issues to the cuprite high-<italic>T</italic>_C superconductivity discovered in 1986. However, the new kind of high-<italic>T</italic>_C superconductivity is beyond the description of the conventional Bardeen–Cooper–Schrieffer (BCS) theory. Here we address these two issues based on the bond order-length-strength correlation and nonbonding electron polarization (BOLS-NEP) notion for the effect of atomic undercoordination and the hydrogen bond (O:H−O equivalent of O:Cu−O) cooperativity and polarizability (HBCP) premise for water ice with involvement of electron lone pairs “:” interactions. First, a Cu^p:O:Cu^p dipolar chain is formed by connecting a series of tetrahedrons made of two Cu⁺ ions and two Cu^p dipoles surrounding the center O^2–. The O−Cu(110) plane includes three sublayers. The first one is made of alternative rows of Cu⁰ vacancies and the Cu^p:O:Cu^p dipolar chain with dipoles pointing out the surface; the second sublayer is formed by O^2– whose lone pairs polarize the dipoles and squeeze out the missing rows of Cu atoms, and the third sublayer is made of Cu⁺. However, the O−Cu(001) plane shows a different manner of the sublayers. The first sublayer is made of Cu^p, Cu⁰, and Cu²⁺, and the third sublayer of Cu⁺ and Cu. The O^2– bonds to the Cu⁺ and polarizes the Cu to form the oppositely-coupled dipoles on the Cu(001) surface. The O−Cu bonding proceeds in four discrete stages: O² bonds to one Cu to form the Cu²⁺−2O^– and then each O^– bonds to its neighboring Cu in the second layer to form the twin tetrahedron with production of the lone pairs. The introduction of O to Cu host creates valence density features of the O−Cu bonding, lone pair nonbonding, the dipolar antibonding above <italic>E</italic>_F, and electron holes. Second, atomic undercoordination of the O−Cu chains and the O−Cu planes shortens and stiffens the local O−Cu bond and lengthens and weakens the O:Cu^p nonbonding interactions associated with further enhancement of the Cu^p dipoles polarization, this process is the same to the O:H−O bond relaxation and polarization occurred to the skins of water and ice. Last, the electron-phonon interaction is realized by the undercoordination-induced bond relaxation and the dual polarization by lone pairs and bond contraction. The dual polarization weakens the O:Cu^p interactions and lowers its vibration frequency of the Cu^p, reducing the effective mass of the Cu^P electrons with high group velocity for carrier transport between the adjacent O−Cu planes that are made of atomic vacancies and dipoles. The self-entrapment of the core and bonding electrons, and the localized polarization and O:Cu^p weakening may describe the effect electron-phonon coupling. The discovered “attraction force” between electrons along the Cu−O chain may fingerprint the effect of atomic undercoordination-induced bond contraction. The understandings of the dual polarization by oxidation and atomic undercoordination of carriers and the electron-phonon interaction may extend to devising the low-dimensional high-<italic>T</italic>_C superconductivity and the edge states polarization for the topological insulator superconductivity. The BOLS-NEP and HBCP regulations could be essential ingredients for the carrier generation and their interactions, which shall play certain substantial roles in the new types of superconductivity.