Screened ion-ion interaction in mercury-chain compounds: Single chain

Abstract

At room temperature, the mercury chains in ${\mathrm{Hg}}_{3\mathrm{-}\mathrm{\delta }}$ ${\mathrm{AsF}}_6$ exhibit phonons characteristic of a one-dimensional lattice. We calculate the screening of the Hg ion-ion interaction in a single chain by electrons moving in a cylindrical potential of finite radius, within the random-phase approximation. The resulting Bohm-Staver-type expression for the phonon velocity is ($Z^2$ ${\mathrm{mN}}_I$/${\mathrm{MN}}_e$ ${)}^{1/2}$ $v_F$, where Z is the Hg ionic charge and $N_I$ ($N_e$) is the number of ions (electrons) per unit length. Use of the Tomonaga-Luttinger solution for the electronic response function (keeping only the small-momentum scattering processes) just renormalizes the Fermi velocity in this expression.