Renormalized model for the dynamics of the krypton-on-graphite domain-wall lattice.

Abstract

The dynamics of an incommensurate monolayer with distinct domain-wall density modulations are considered, and a renormalized model is presented that accurately describes the phason-like vibrational behavior of the domain-wall network. The domain walls are shown to vibrate as strings. The string wave velocity is found to be essentially independent of the width of the walls or, in other words, of the amplitude of the substrate corrugation. For krypton on graphite it is about 600 m ${\mathrm{s}}^{\mathrm{\ensuremath{-}}1}$. The vibrational modes of the network are determined by the vertices, which provide the boundary conditions for the domain-wall segments. Matching the results of the model with a normal-mode calculation for the krypton-on-graphite system [Phys. Rev. B 34, 7334 (1986)], the following parameters are determined for the vertices; (i) effective mass, (ii) moment of inertia, (iii) effective radius, (iv) vertex-vertex interaction, and (v) restoring torque exerted by the substrate when walls move away from a symmetry direction of the substrate (this torque can be weakened significantly when the domain-wall size decreases because of overcompression at the vertices). Analytic expressions are available for the first two quantities. Anharmonic effects of the adatom interaction are found to alter the vibrational-mode energies of the domain walls from those obtained by a quasiharmonic calculation for the motion of the adatoms. The limit is also taken towards very large domain size, where the solutions to the dynamical matrix become relatively simple. Thermodynamic quantities such as the specific heat, which can be calculated from the vibrational-mode spectrum, show no discontinuity at the commensurate-incommensurate transition. Near the transition the sound velocities for the domain-wall lattice have very simple expressions.