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Tunneling and Strong-Coupling Superconductivity
Published in R. D. Parks, Superconductivity, 2018
The physical model of a metal considered by Bardeen, Cooper, and Schrieffer (3) in their original paper is the picture that was formalized by Landau (35) and known as the Fermi liquid theory. It is assumed that the lowlying electronic excitations are long-lived quasi-particles, in one-to-one correspondence with the excitations of the free Fermi gas, and that these fully dressed quasi-particles have some residual interaction. In a metal there are two contributions to this interaction: (1) the exchange of virtual phonons which produces an attractive interaction between quasi-particles provided their energy is less than the phonon energy, and (2) the screened Coulomb interaction, which is repulsive. BCS showed by a variational calculation that, when this residual interaction is attractive at the Fermi surface, a new superconducting ground state, with pairs of electrons bound into Cooper pairs, is energetically more favorable than the normal state. For this purpose BCS chose a model interaction equal to − V when the kinetic energy of both quasi-particles is less than a typical phonon energy and zero otherwise. With the interaction parameter chosen phenomenologically the BCS model is in remarkably good agreement with a wide variety of experiments. The underlying physical model, the Landau Fermi liquid theory, is valid only for temperatures and excitation energies much less than a typical phonon energy. The lifetime of an electron with enough energy to emit real phonons is very short so that the quasi-particle is not well defined. One finds deviations from the BCS model for the “strong-coupling” superconductors, Pb and Hg, where the transition temperature is high enough and Debye temperature low enough for the Fermi liquid theory to fail.
Ultrafast Electron–Phonon Coupling at Metal-Dielectric Interface
Published in Heat Transfer Engineering, 2019
Qiaomu Yao, Liang Guo, Vasudevan Iyer, Xianfan Xu
The subscripts i are 0, 1, and 2 for the Drude term and the two Lorentz terms, respectively. For the damping factor in the Drude model Γ0, the coefficient describing electron–electron scattering Aee0 is taken as 1.2 × 107 s−1K−2 which is obtained from the low temperature Fermi liquid theory [20]. Bep0 is chosen as 3.6 × 1011 s−1K−1 which is predicted by matching the experimental results of dielectric constant at room temperature [21]. The electron–electron scattering rate of Lorentzian oscillators Aee1, Aee2 are assumed to be the same as those in the Drude model Aee0. Bep1,Bep2 are determined using room temperature optical constants with Eq. (7) [17]. We also found that a temperature-independent term Yi needs to be included for the Lorentzian oscillators (Y0 is taken to be 0), in order to fit the entire optical response. Y1, Y2 are found to be 7.9 × 1014 rad/s and 1.9 × 1015 rad/s, respectively. All the parameters are listed in Table 1.
Effect of the nonmonotonic d-wave superconducting gap on the electronic Raman scattering of electron-doped cuprate superconductors
Published in Philosophical Magazine, 2020
Yuchen Zhang, Sheng Xu, Feng Yuan, Huaisong Zhao, Yong Zhou
The cuprate superconductors can be classified into two categories, hole-doped and electron-doped cuprates [1,2]. Although the superconducting transition temperatures of electron-doped cuprate superconductors are 30K at most, it is very important to systematically study the unconventional physical properties in electron-doped cuprate superconductors due to many similarities and differences with hole-doped cuprate superconductors [2,3]. The superconductivity in both electron-doped and hole-doped cuprate superconductors happens in the CuO plane and belongs to the unconventional cases which can not be explained within the framework of the Fermi-liquid theory. The parent of both hole-doped and electron-doped cuprates are Mott insulators with an antiferromagnetic long-range order (AFLRO). The AFLRO can be destroyed by doping holes or electrons, and it disappears at the critical doping concentration, then the antiferromagnetic short-range order (AFSRO) correlation plays an important role in superconductivity [4–6]. The phase diagram of electron-doped cuprate superconductors as a function of doping, however, are different from the hole-doped case [2,7–13], which shows the particle-hole asymmetry in a doped Mott insulator. Moreover, the existence of AFLRO in electron-doped cuprate superconductors has a wider doping range than the hole-doped case, and even the AFLRO of electron-doped cuprate superconductors coexists with superconductivity over some range of the electron doping concentration. Therefore, the phase separation between AFLRO and superconductivity is not clear in electron-doped cuprate superconductors. Moreover, the electronic structure of electron-doped cuprates shows some unique characteristics by the angle-resolved photoemission spectroscopy (ARPES), nuclear magnetic resonance (NMR) and Shubnikov–de Haas (SdH) oscillations [12–17]. In particular, the superconducting (SC) gap symmetry between electron-doped and hole-doped cuprate superconductors has an apparent discrepancy. Electron-doped cuprate superconductors have a nonmonotonic d-wave SC gap function [18–23], which is different from hole-doped cuprate superconductors with a pure d-wave SC gap symmetry [24–30].