Effective Theory of Superconductivity in Strongly-Coupled Amorphous Materials

Abstract

A theory of phonon-mediated superconductivity in strong-coupling amorphous materials is developed based on an effective description of structural disorder and its effect on the vibrational spectrum. The theory accounts for the diffusive-like transport of vibrational excitations due to disorder-induced scattering within the Eliashberg theory of strong-coupling superconductivity. The theory provides a good analytical description of the Eliashberg function ${\alpha }^{2}F(\omega )$ in comparison with experiments, and allows one to disentangle the effects of transverse and longitudinal excitations on the Eliashberg function. In particular, it shows that the transverse excitations play a crucial role in driving an increase or excess in the Eliashberg function at low energy, which is related to the boson peak phenomenon in vibrational spectra of glasses. This low-energy excess, on one hand drives an enhancement of the electron-phonon coupling but at the same time reduces the characteristic energy scale ${\omega }_{log}$ in the Allen-Dynes formula. As a consequence, the non-monotonicity of $T_c$ as a function of alloying (disorder) in $\text{Pb}$-based systems can be rationalized. The case of $\text{Al}$-based systems, where disorder increases $T_c$ from the start, is also analyzed. General material-design principles for enhancing $T_c$ in amorphous superconductors are presented.

matching the final version published in PRB

References in corpus (3)

• The Ioffe-Regel criterion and diffusion of vibrations in random lattices
• Unified theory of vibrational spectra in amorphous materials
• Glass-induced enhancement of superconducting $T_c$: Pairing via dissipative mediators

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• Spectral properties and enhanced superconductivity in renormalized Migdal-Eliashberg theory
• Quantum confinement theory of ultra-thin films: electronic, thermal and superconducting properties
• Plasmon energy losses in shear bands of metallic glass
• Microscopic mechanism of electric field-induced superconductivity suppression in metallic thin films
• Pressure-induced concurrent amorphization and superconductivity in topological material NbNiTe5