Phonon mediated superconductivity in low carrier-density systems

Abstract

Motivated by the observation of superconductivity in SrTiO${}_3$ and Bi, we analyze phonon-mediated superconductivity in three-dimensional systems at low carrier density, when the chemical potential $\mu$ (equal to Fermi energy at $T=0$) is comparable to or even smaller than the characteristic phonon frequency ${\omega }_L$. We consider the attractive part of the Bardeen-Pines pairing interaction, in which the frequency-dependent electron-phonon interaction is dressed by the Coulomb potential. This dressing endows the pairing interaction with momentum dependence. We argue that the conventional Migdal-Eliashberg (ME) approximation becomes invalid when $\mu \le {\omega }_L$ chiefly because the dominant contribution to pairing comes from electronic states away from the Fermi surface. We obtain the pairing onset temperature, which is equal to $T_c$ in the absence of phase fluctuations, as a function of $\mu /{\omega }_L$. We find both analytically and numerically that $T_c$ increases as the ratio $\mu /{\omega }_L$ becomes smaller. In particular, in the dilute regime, $\mu \to 0$, it holds that $T_c\propto {\omega }_L{\left(\frac{Ry}{{\omega }_L}\right)}^{\eta }$, where $\text{Ry}$ is the Rydberg constant and $\eta \sim 0.2$.

10 pages, 6 figures

References in corpus (7)

• Unconventional pairing originating from disconnected Fermi surfaces in superconducting LaFeAsO${}_{1-x}$F${}_x$}
• Magnetism, superconductivity, and pairing symmetry in Fe-based superconductors
• Topological $R$PdBi half-Heusler semimetals: a new family of non-centrosymmetric magnetic superconductors
• Low-energy microscopic models for iron-based superconductors: a review
• Superconductivity in three-dimensional spin-orbit coupled semimetals
• Pairing from dynamically screened Coulomb repulsion in bismuth
• Antiadiabatic phonons, Coulomb pseudopotential and superconductivity in Eliashberg - McMillan theory

Cited by in corpus (7)

• Relative importance of nonlinear electron-phonon coupling and vertex corrections in the Holstein model
• Gap Anisotropy in Multiband Superconductors Based on Multiple Scattering Theory
• Kohn-Luttinger Correction to Tc in a Phonon Superconductor
• Electron-phonon coupling and superconductivity in the doped topological-crystalline insulator (Pb${}_{0.5}$Sn${}_{0.5}$)${}_{1-x}$In${}_x$Te
• Domes of $T_c$ in single-band and multiband superconductors with finite-range attractive interactions
• Dynamical vortices in electron-phonon superconductors
• The Effect of Repulsion on Superconductivity at Low Density