Frenkel-Kontorowa Model with Deformable Substrate: Ground State and Excitation Spectrum

Abstract

A self-consistent model of two interpenetrating deformable chains is proposed to exactly calculate the ground state and the excitation spectrum in the continuum limit. Transformation from incommensurate state to commensurate state continuously occurs for the out-of-phase coordinate (W), implying that the transformation simultaneously occurs on both chains, where deformability makes the transformation easier. The in-phase coordinate (Q), however, is rigid. The excitation spectrum consists of two independent modes, obtained as the interacting modes between W and Q through the kinetic coupling. These modes have their own gaps at the inverse kink length. For no kinetic coupling, Q possesses no gap, though W still maintains the gap.