Superconductivity near lattice instability: the case of NbC$_{1-x}$N$_x$ and NbN

TL;DR

This study uses density functional theory to analyze how lattice instabilities and electron-phonon interactions influence the superconducting transition temperature in NbC$_{1-x}$N$_x$ and NbN, revealing the role of phonon anomalies.

Contribution

It introduces a model separating unstable phonon effects to explain the increase in $T_c$ near structural instability in NbC$_{1-x}$N$_x$ and NbN.

Findings

Electron-phonon coupling is enhanced by Fermi surface nesting.

$T_c$ increases from 11.2 K to 17.3 K with nitrogen doping.

A model reproduces $T_c$ rise near the structural phase transition.

Abstract

Using density functional theory within the local density approximation we report a study of the electron-phonon coupling in NbC$_{1-x}$N$_x$ and NbN crystals in the rocksalt structure. The Fermi surface of these systems exhibits important nesting. The associated Kohn anomaly greatly increases the electron-phonon coupling and induces a structural instability when the electronic density of states reaches a critical value. Our results reproduce the observed rise in $T_{c}$ from 11.2 K to 17.3 K as the nitrogen doping is increased in NbC$_{1-x}$N$_x$. To further understand the contribution of the structural instability to the rise of the superconducting temperature, we develop a model for the Eliashberg spectral function in which the effect of the unstable phonons is set apart. We show that this model together with the McMillan formula can reproduce the increase of $T_{c}$ near the structural phase transition.