Polaronic behavior in a weak coupling superconductor

TL;DR

This study investigates the superconducting behavior of Nb-doped SrTiO$_3$, revealing weak electron-phonon coupling in the superconducting state despite strong interactions in the normal state, challenging conventional theories.

Contribution

The paper provides direct spectroscopic evidence of weak coupling in the superconducting state of SrTiO$_3$, highlighting the role of high-energy phonons and offering insights into its unconventional superconductivity.

Findings

Strong coupling to high-energy LO phonons in the normal state.

Superconducting gap consistent with weak-coupling BCS theory.

High-energy phonons do not dominate pairing in SrTiO$_3$.

Abstract

The nature of superconductivity in the dilute semiconductor SrTiO$_3$ has remained an open question for more than 50 years. The extremely low carrier densities ($10^{18}$ - $10^{20}$ cm$^{-3}$) at which superconductivity occurs suggests an unconventional origin of superconductivity outside of the adiabatic limit on which the Bardeen-Cooper-Schrieffer (BCS) and Migdal-Eliashberg (ME) theories are based. We take advantage of a newly developed method for engineering band alignments at oxide interfaces and access the electronic structure of Nb-doped SrTiO$_3$ using high resolution tunneling spectroscopy. We observe strong coupling to the highest energy longitudinal optic (LO) phonon branch and estimate the doping evolution of the dimensionless electron-phonon interaction strength ($\lambda$). Upon cooling below the superconducting transition temperature ($T_{\mathrm{c}}$), we observe a single superconducting gap corresponding to the weak-coupling limit of BCS theory, indicating an order of magnitude smaller coupling ($\lambda_{\textrm{BCS}} \approx 0.1$). These results suggest that despite the strong normal state interaction with electrons, the highest LO phonon does not provide a dominant contribution to pairing. They further demonstrate that SrTiO$_3$ is an ideal system to probe superconductivity over a wide range of carrier density, adiabatic parameter, and electron-phonon coupling strength.