Phonon-mediated electron attraction in SrTiO$_3$ via the generalized Fr\"ohlich and deformation potential mechanisms

TL;DR

This paper presents a theoretical framework showing that phonon-mediated interactions, including a generalized Fr"ohlich mechanism and deformation potential, can explain superconductivity in SrTiO$_3$, highlighting the role of lattice dynamics.

Contribution

The study introduces a combined theoretical and first-principles approach to demonstrate phonon-mediated electron attraction mechanisms in SrTiO$_3$, expanding understanding of superconductivity in doped semiconductors.

Findings

Long-range electron-phonon coupling can induce superconductivity in SrTiO$_3$

Deformation potential mechanism contributes additional electron attraction

Theoretical results align with experimental observations of superconductivity

Abstract

Superconductivity in doped SrTiO$_3$ was discovered in 1964, the first superconducting transition observed in a doped semiconductor. However, the mechanism of electron pairing in SrTiO$_3$ remains a subject of debate. By developing a theoretical framework to incorporate dynamical lattice screening in the electronic Coulomb interactions of semiconductors and insulators, we demonstrate analytically that linear long-range coupling of electrons to multiple longitudinal optical phonons, described by a generalized Fr\"ohlich mechanism, can result in superconductivity in SrTiO$_3$. Moreover, by combining our theory with first-principles calculations, we reveal an additional attractive interaction between electrons in SrTiO$_3$ due to the deformation potential mechanism, arising from the mixed ionic-covalent character of the Ti-O bond. Our results may have implications for the emergence of phonon-mediated electron attraction and superconductivity in a broad range of materials.