Relationship betweenTcandN(0): An NMR study ofV3Ga1−xSix

From the measured normal-state values of the ${}_{}{}^{51}{}_{}{}^{}\mathrm{V}$ spin-lattice relaxation rate and nuclear-electric-quadrupole interaction in ${\mathrm{V}}_3{\mathrm{Ga}}_{1-x}{\mathrm{Si}}_x$, we have determined the bare electronic density of states at the Fermi level, $N\left(0\right)\mathrm{}$, using a tight-binding formalism. In the high-$T_c$ compositions, $N\left(0\right)\mathrm{}$ is dominated by the $\pi$-symmetry $d$ subband that can be thought of as a narrow virtually localized state on the vanadium atoms (half-width ≅ 20 mRy) which is broadened by compositional fluctuations. It is found that the superconducting transition temperature normalized by the Debye temperature ($\frac{T_c}{{\Theta }_D}$) for the ${\mathrm{V}}_3{\mathrm{Ga}}_{1-x}{\mathrm{Si}}_x$ and ${\mathrm{V}}_3{\mathrm{Ga}}_{1-x}{\mathrm{Sn}}_x$ compounds is a universal function of $N\left(0\right)\mathrm{}$. The relationship between the mass renormalization $\lambda$ and $N\left(0\right)\mathrm{}$ is considered in terms of the renormalization of the phonon frequencies due to electronic screening.