Coulomb Gap in Sodium Tungsten Bronzes

Abstract

Recent photoemission experiments on sodium tungsten bronzes, ${\mathrm{Na}}_{x}{\mathrm{Ta}}_{y}{\mathrm{W}}_{1\ensuremath{-}y}{\mathrm{O}}_{3}$, have revealed a depletion of the density of states near the chemical potential in insulating samples. We propose that this depletion is a Coulomb gap, and that these experiments represent the first direct measurement of a Coulomb gap in a disordered insulator. Our conclusion is supported by physical estimates and numerical calculations of the density of states for a classical model of ${\mathrm{Na}}_{x}{\mathrm{Ta}}_{y}{\mathrm{W}}_{1\ensuremath{-}y}{\mathrm{O}}_{3}$. The width and shape of the calculated bands agree well with the experiments.