Low-density superconductivity in SrTiO$_3$ bounded by the adiabatic criterion

TL;DR

This study investigates low-density superconductivity in SrTiO$_3$, revealing that superconductivity persists in the anti-adiabatic regime and is likely mediated by a soft transverse-optic phonon mode related to ferroelectric instability.

Contribution

It provides high-resolution tunneling spectroscopy data showing the alignment of the superconducting boundary with the Fermi energy crossing the Debye energy, and proposes a pairing mechanism involving a soft phonon mode.

Findings

Superconductivity persists down to very low densities in SrTiO$_3$.

The superconducting boundary aligns with the Fermi energy crossing the Debye energy.

A soft transverse-optic phonon mode may mediate pairing in the anti-adiabatic regime.

Abstract

SrTiO$_3$ exhibits superconductivity for carrier densities $10^{19}-10^{21}$ cm$^{-3}$. Across this range, the Fermi level traverses a number of vibrational modes in the system, making it ideal for studying dilute superconductivity. We use high-resolution planar-tunneling spectroscopy to probe chemically-doped SrTiO$_3$ across the superconducting dome. The over-doped superconducting boundary aligns, with surprising precision, to the Fermi energy crossing the Debye energy. Superconductivity emerges with decreasing density, maintaining throughout the Bardeen-Cooper-Schrieffer (BCS) gap to transition-temperature ratio, despite being in the anti-adiabatic regime. At lowest superconducting densities, the lone remaining adiabatic phonon van Hove singularity is the soft transverse-optic mode, associated with the ferroelectric instability. We suggest a scenario for pairing mediated by this mode in the presence of spin-orbit coupling, which naturally accounts for the superconducting dome and BCS ratio.