# High-$T_c$ superconductivity in weakly electron-doped HfNCl

## TL;DR

This study explores how electron doping in Li$_x$HfNCl enhances superconductivity, revealing a strong doping-dependent increase in critical temperature linked to electron-electron interactions and intervalley phonon coupling.

## Contribution

It provides a detailed theoretical analysis of the doping-dependent superconducting properties of Li$_x$HfNCl, highlighting the role of electron-electron interactions and disorder effects in high-$T_c$ superconductivity.

## Key findings

- Superconducting $T_c$ reaches up to 40 K at low doping levels.
- Spin susceptibility is strongly enhanced at low doping due to electron-electron interactions.
- Disorder and Anderson localization compete with superconductivity, affecting $T_c$.

## Abstract

We investigate the magnetic and superconducting properties in electron-doped Li$_x$HfNCl. HfNCl is a band insulator that undergoes an insulator to superconductor transition upon doping at $x\approx0.13$. The persistence of the insulating state for $x<0.13$ is due to an Anderson transition probably related to Li disorder. In the metallic and superconducting phase, Li$_x$HfNCl is a prototype two-dimensional two-valley electron gas with parabolic bands. By performing a model random phase approximation approach as well as first-principles range-separated Heyd-Scuseria-Ernzerhof (HSE06) calculations, we find that the spin susceptibility $\chi_s$ is strongly enhanced in the low doping regime by the electron-electron interaction. Furthermore, in the low doping limit, the exchange interaction renormalizes the intervalley electron-phonon coupling and results in a strong increase of the superconducting critical temperature for $x<0.15$. On the contrary, for $x>0.15$, $T_c$ is approximately constant, in agreement with experiments. At $x=0.055$ we found that $T_c$ can be as large as 40 K, suggesting that the synthesis of cleaner samples of Li$_x$HfNCl could remove the Anderson insulating state competing with superconductivity and generate a high-$T_c$ superconductor.