Concentration-Dependent Kohn Effect in Cubic Tungsten Bronzes

Inelastic neutron scattering measurements on single crystals of cubic ${\mathrm{Na}}_x\mathrm{W}{\mathrm{O}}_3$ reveal a large concentration-dependent Kohn anomaly in the [100] longitudinal acoustic-phonon dispersion curve. The results demonstrate the two-dimensional character of the Fermi surface, support the rigid-band model for $0.56<x<\mathrm{}0.83\mathrm{}$, and conflict with the percolation model which has just recently been proposed to explain the transport properties of the tungsten bronzes.