Enhancement of superconductivity and its relation to lattice expansion in InTe

The quest to govern the driving forces behind superconductivity and gain control over the superconducting transition temperature $T_{c}$ is as old as the phenomenon itself. Microscopically, this requires a proper understanding of the evolution of electron-lattice interactions in their parameter space. We report such a controlled study on $T_{c}$ in In$_{x}$Te via fine-tuning the In stoichiometry $x$. We find that increasing $x$ from 0.84 to 1 results in an enhancement of $T_{c}$ from 1.3 K to 3.5 K accompanied by an increase of the electron-phonon coupling constant from 0.45 to 0.63. Employing first-principles calculations, we show that this behavior is driven by two factors, each taking the dominant role depending on $x$. For $x\lesssim 0.92$, the major role is played by the density of electronic states at the Fermi level. Above $x\sim 0.92$, the change in the density of states flattens while the enhancement of $T_{c}$ continues. We attribute this to a systematic softening of lattice vibrations, amplifying the electron-phonon coupling, and hence, $T_{c}$.