Interband Electron Pairing for Superconductivity from the Breakdown of the Born‐Oppenheimer Approximation

Abstract

The origin of interband electron pairing, responsible for enhancing superconductivity, and the factors controlling its strength were examined. We show that interband electron pairing is a natural consequence of breaking down the Born-Oppenheimer approximation during electron-phonon interactions. Its strength is determined by the pair-state excitations around the Fermi surfaces that take place to form a superconducting state. Fermi surfaces favorable for the pairing were found, and the implications of this observation are discussed.Since the discovery of superconductivity in Hg at 4 K in 1911, [1] numerous studies have been carried out to find other superconductors with higher superconducting transition temperature T c and understand the cause for superconductivity. The charge carriers of superconductors are pairs of electrons while those of normal metals are individual electrons. The Bardeen-Cooper-Schrieffer (BCS) theory of superconductivity, [2] in which the electron pairing arises from electron-phonon interactions, showed that the T c increases with raising the average phonon frequency hwi of the lattice, the electronic density of states (DOS) at the Fermi level n(e F ) and the electron-phonon coupling constant l. By explicitly taking into consideration the actual electron-phonon interactions and the Coulomb repulsion between pairing electrons, Eliashberg extended the BCS theory to show the relationship of T c to the effective Coulomb repulsion m* and the electron-phonon spectral function a 2 (w) F(w). [3,4] McMillan numerically solved the Eliashberg equations as a function of m* and a 2 (w) F(w) in a small range of m* and l to express T c as an exponential function of l and m* with the prefactor V D /1.45, where V D is the Debye temperature. [5] The McMillan equation was improved by Allen and Dynes [6] by modifying the prefactor such that all parameters constituting the prefactor can be calculated once the spectral function a 2 (w) F(w) is known. Thus, with typical value of m* = 0.13, one can predict the T c of any metal on the basis of the Allen-Dynes

Superconducting and Superhard Ice

“…[36][37][38] Therefore, we evaluate the bulk modulus, shear modulus and the Viker hardness of ice structures Pmc2 1 , P2 1 and C2/m with incremental pressures, according to Eq. (7). With the increase of pressure, the three phases give rise to the repulsion by the valence electrons that come from the core electrons.…”

“…[1][2] The electron-phonon mechanism of superconductivity was proposed based on the Bardeen-Cooper-Schrieffer (BCS) theory, [5] which is a single band model and does not take into account the multiband nature of the actual electronic structures. The multiband effect has been previously studied by Suhl et al [6] and Whangbo et al [7] The McMillan equation and its variations are essential empirical relations between critical temperature of superconductor and other parameters such as the effective electron-phonon coupling constant (λ). These equations contain part of the contributions of the multiband effect based on the realistic electronic structures, thereby provide feasible ways for theoretical prediction of superconducting materials and enable recent works of superconductor.…”

“…The multiband effect has been previously studied by Suhl et al . and Whangbo et al . The McMillan equation and its variations are essential empirical relations between critical temperature of superconductor and other parameters such as the effective electron‐phonon coupling constant (λ).…”

Are Superconductivity Mechanisms a Matter for Chemists?

“…Such a behavior can be considered as the result of the O(2p)/O(2s) hybridization (Figure 6c). This dipole oscillation may contribute, as in atomic spinodes, to induce a decomposition into various components of the e u /b 1 mixtures in equilibrium, exchanging hole pairs, and consequently leading to the Whangbo Hamiltonian of pair-occupied and pair-unoccupied states [23,43].…”

“Flat/steep band model” for superconductors containing Bi square nets

“…These two kinds of electrons interact with phonons in a very different way [20,21], and thus naturally lead to a two-band superconductivity mechanism [22] for conventional superconductors. The inter-band pairing which is important for enhancing T C was shown to be due to the breakdown of the Born-Oppenheimer approximation by Whangbo et al [23]. Recently, Deng et al have shown that the generalized coherent state constructed by pure group theory can be used to describe the superconducting state.…”