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Register a new userExtending the theory of phonon-mediated superconductivity in quasi-2D
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J.P.Hague
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I present results from an extended Migdal-Eliashberg theory of electron-phonon interactions and superconductivity. The history of the electron-phonon problem is introduced, and then study of the intermediate parameter regime is justified from the energy scales in the cuprate superconductors. The Holstein model is detailed, and limiting cases are examined to demonstrate the need for an extended theory of superconductivity. Results of the extended approximation are shown, including spectral functions and phase diagrams. These are discussed with reference to Hohenbergs theorem, the Bardeen-Cooper-Schrieffer theory and Coulomb repulsion.
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We develop a strong-coupling theory of Bose-Einstein condensate-mediated superconductivity in a hybrid system, which consists of a two-dimensional electron gas with either (i) parabolic spectrum or (ii) relativistic Dirac spectrum in the vicinity of a two-dimensional solid-state condensate of indirect excitons. The Eliashberg equations are derived and the expressions for the electron pairing self-energy due to the exchange interaction between electrons mediated by a single Bogoliubov excitation (a bogolon) and the bogolon pairs are found. Furthermore, we find the superconducting order parameter and estimate the critical temperature of the superconducting transition. The critical temperature reveals its linear dependence on the dimensionless coupling constant. It is shown, that the bogolon-pair-mediated interaction is the dominant mechanism of electron pairing in hybrid systems in both the weak and strong coupling regimes. We calculate the effective bogolon-electron interaction constant for both parabolic and linear electron dispersions and examine the dependence of the critical temperature of electron gas superconducting transition on exciton condensate density.
We present a theory of phonon-mediated superconductivity in near magic angle twisted bilayer graphene. Using a microscopic model for phonon coupling to moire band electrons, we find that phonons generate attractive interactions in both $s$ and $d$ wave pairing channels and that the attraction is strong enough to explain the experimental superconducting transition temperatures. Before including Coulomb repulsion, the $s$-wave channel is more favorable; however, on-site Coulomb repulsion can suppress $s$-wave pairing relative to $d$-wave. The pair amplitude varies spatially with the moire period, and is identical in the two layers in the $s$-wave channel but phase shifted by $pi$ in the $d$-wave channel. We discuss experiments that can distinguish the two pairing states.
If history teaches us anything, it is that the next breakthrough in superconductivity will not be the result of surveying the history of past breakthroughs, as they have almost always been a matter of serendipity resulting from undirected exploration into new materials. Still, there is reason to reflect on recent advances, work toward higher T_c of even an incremental nature, and recognize that it is important to explore avenues currently believed to be unpromising even as we attempt to be rational. In this paper we look at two remarkable new unusually high temperature superconductors (UHTS), MgB2 with Tc=40 K and (in less detail) high pressure Li with Tc=20 K, with the aim of reducing their unexpected achievements to a simple and clear understanding. We also consider briefly other UHTS systems that provide still unresolved puzzles; these materials include mostly layered structures, and several with strongly bonded C-C or B-C substructures. What may be possible in phonon-coupled superconductivity is reconsidered in the light of the discussion.
We consider an s-wave superconductor in the vicinity of a second-order ferromagnetic (FM) or spin-density-wave (SDW) quantum critical point (QCP), where the superconductivity and magnetism arise from separate mechanisms. The quantum critical spin fluctuations reduce the superconducting T_c. Near a FM QCP, we find that T_c falls to zero as 1/|ln kappa| in 3D and as kappa in 2D, where kappa ~ |J-J_c|^nu is the inverse correlation length of the spin fluctuations, and measures the distance |J-J_c| from the quantum critical point. SDW quantum critical fluctuations, on the other hand, suppress T_c to zero as sqrt(kappa) in 2D, and suppress T_c only to a finite value in 3D, producing a cusp of the form (const + |J-J_c|^nu).
We use a Luttinger-Ward functional approach to study the problem of phonon-mediated superconductivity in electron systems with strong electron-electron interactions (EEIs). Our derivation does not rely on an expansion in skeleton diagrams for the EEI and the resulting theory is therefore nonperturbative in the strength of the latter. We show that one of the building blocks of the theory is the irreducible six-leg vertex related to EEIs. Diagrammatically, this implies five contributions (one of the Fock and four of the Hartree type) to the electronic self-energy, which, to the best of our knowledge, have never been discussed in the literature. Our approach is applicable to (and in fact designed to tackle superconductivity in) strongly correlated electron systems described by generic lattice models, as long as the glue for electron pairing is provided by phonons.
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