Strong electron-phonon coupling and phonon-induced superconductivity in tetragonal C$_3$N$_4$ with hole doping

TL;DR

This study predicts that hole-doped tetragonal C$_3$N$_4$ exhibits strong electron-phonon coupling leading to phonon-induced superconductivity with a potential critical temperature of around 36 K, depending on hole concentration.

Contribution

First-principles calculations reveal that hole doping induces superconductivity in C$_3$N$_4$, highlighting a new pathway for high-temperature superconductivity in this material.

Findings

Hole doping causes strong electron-phonon coupling in C$_3$N$_4$.

Superconductivity with a critical temperature up to 36 K is predicted.

Boron doping can effectively inject holes without altering electronic structure.

Abstract

C$_3$N$_4$ is a recently discovered phase of carbon nitrides with the tetragonal crystal structure [D.Laniel $\textit{et al.}$, Adv. Mater. 2023, 2308030] that is stable at ambient conditions. C$_3$N$_4$ is a semiconductor exhibiting flat-band anomalies in the valence band, suggesting the emergence of many-body instabilities upon hole doping. Here, using state-of-the-art first-principles calculations we show that hole-doped C$_3$N$_4$ reveals strong electron-phonon coupling, leading to the formation of a gapped superconducting state. The phase transition temperatures turn out to be strongly dependent on the hole concentration. We propose that holes could be injected into C$_3$N$_4$ via boron doping which induces, according to our results, a rigid shift of the Fermi energy without significant modification of the electronic structure. Based on the electron-phonon coupling and Coulomb pseudopotential calculated from first principles, we conclude that the boron concentration of 6 atoms per nm$^3$ would be required to reach the critical temperature of $\sim$36 K at ambient pressure.