Phonon Softening in Two-Dimensional Electron-Lattice System with Anisotropy(Condensed matter : electronic structure and electrical, magnetic, and optical properties)

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The effect of anisotropy on phonon softening at finite temperatures in a two-dimensional (2D) electron-lattice system is studied numerically. On the basis of the Su-Schrieffer-Heeger model generalized to a 2D system with a half-filled electronic band on the square lattice, we introduce an anisotropy parameter γ in the electronic transfer integrals and the electron-lattice coupling constants in the x and y directions, t_x and t_y, and α_x and α_y, respectively, as t_x/t_y=α_x/α_y=(1+γ/2)/(1-γ/2). In the isotropic system, it has been shown that the phonon frequencies of transverse modes with the nesting vector Q=(π/a, π/a) (a is the lattice constant) and with wave vectors parallel to Q, and that of the longitudinal mode with Q are all softened at the same Peierls transition temperature. In the presence of anisotropy, it is found that the mode with Q having its amplitude only in the strong-coupling direction is softened first as the temperature is lowered in the metallic phase while other modes are still only partially softened. This is qualitatively different from the Peierls transition in the isotropic system. When the temperature is decreased further in the presence of distortion in the strong-coupling direction with the wave vector Q, the mode related to the wave vector q_<min>=(2π/Na, 2π/Na) (N is the linear dimension of the system) is softened first.
社団法人日本物理学会の論文
2007-11-15