Electronic stiffness of a superconducting niobium nitride single crystal under pressure

We report a quantitative study of pressure effects on the superconducting transition temperature $T_c$ and the electronic stiffness of niobium nitride. It is found that $T_c$ increases initially with pressure and then saturates up to $42\mathrm{GPa}$. Combining phonon and structural information on the samples obtained from the same single crystal, we derive a nonmonotonic pressure dependence of the electronic stiffness, rising moderately at low pressure while dropping slightly at high pressure. The theory of Gaspari and Gyorffy is found to reproduce the observed low-pressure results qualitatively but fails to predict the high-pressure data. The observed pressure effect on $T_c$ is attributed to the pressure-induced interplay of the electronic stiffness and phonon frequencies.

Figure 1

Magnetic susceptibility signal vs temperature for a $\mathrm{Nb}{\mathrm{N}}_{0.90\left(1\right)}$ single crystal at various pressures. The superconducting transition temperature $T_c$ is marked by an arrow.

Figure 2

Dependence of the superconducting transition temperature $T_c$ on pressure in a $\mathrm{Nb}{\mathrm{N}}_{0.90\left(1\right)}$ single crystal. The error bars give the transition onset uncertainty. The solid curve is a fit to the experimental data.

Figure 3

(Color online) Plot of the calculated density of states vs energy of NbN at different pressures. Inset: density of states at the Fermi level $N\left(E_F\right)$ as a function of pressure in NbN. The solid line is a fit to the calculated data.

Figure 4

Pressure dependence of the phonon frequency of the acoustic branch ${⟨{\omega }_{\mathit{ac}}^2⟩}^{1∕2}$ in a $\mathrm{Nb}{\mathrm{N}}_{0.90\left(1\right)}$ single crystal deduced from high-pressure Raman data (Ref. 19). The solid curve is a fit to the data points.

Figure 5

Pressure dependence of the normalized electronic stiffness $N\left(E_F\right)⟨I^2⟩$ of niobium nitride up to $30\mathrm{GPa}$.