Peierls Transition and Nonlinear Localized Excitations in Two-dimensional Electron-Lattice System

二维电子晶格系统中的 Peierls 跃迁和非线性局域激发

基本信息

批准号：
14540365
负责人：
ONO Yoshiyuki
金额：
$ 1.47万
依托单位：
Toho University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2003
项目状态：
已结题

项目摘要

The purpose of the present project was initially to study the structure and the dynamics of nonlinear localized excitations in 2D electron-lattice systems like solitons or polarons seen in 1D systems as polyacetylene. We had to start with investigating the ground state structure which would give the background for such excitations. To our surprise, the so far known ground state in 2D square lattice electron-lattice system with a half-filled electronic band was not a real ground state. In earlier studies a single mode Peierls state involving only the distortion modes with the nesting vector was considered. In our present study, it has been shown that the true ground state involves not only the nesting vector modes but also many other modes having wave vectors parallel to the nesting vector. It was argued that this multimode Peierls state is realized by second order nesting processes which use electronic states not lying on the Fermi surface as intermediate states. Furthermore we have fo … More und that there are many non-equivalent distortion patterns which give the same ground state energy and that the energy gap in the electronic dispersion does not vanish at any point on the Fermi surface in contrast to the single mode Peierls phase. These features are maintained even at finite temperatures and all the distortion modes vanish at the same transition, temperature when the temperature is increased from the absolute zero. The transition temperature depends on the electron-lattice coupling constant but not on the distortion pattern. This transition is also found to be accompanied by softening of phonon modes. The softening occurs at the transition temperature and the relevant modes are the longitudinal and transverse modes with the nesting vector and the transverse modes with wave vectors parallel to the nesting vector. In the low temperature region where the multimode Peierls distortions are present, the phonon dispersion seems dependent on the distortion pattern.As for the nonlinear excitations we have analyzed only the acoustic polaron in 2D square lattice. The acoustic polaron is stabilized only when the electron-lattice coupling constant exceeds a critical value. If we accelerate the polaron by an external electric field, the extent of the polaron shrinks similarly as in 1D case. Furthermore there is a maximum value of the velocity of a stable polaron, which is about 10% of the sound velocity. The effective mass as well as the maximum velocity shows anisotropy reflecting the square structure of the background lattice. Less

本项目的目的最初是为了研究2D电子静态系统（如固体或1D系统中的极性系统）中非线性局部兴奋的结构和动力学。我们必须从研究基态结构开始，这将为这种兴奋提供背景。令我们惊讶的是，到目前为止，迄今为止已知的基态晶格电子晶格系统具有半填充的电子带，这不是真正的基态。在较早的研究中，单个模式PEIERLS状态仅涉及带有嵌套载体的失真模式。在我们目前的研究中，已经表明，真正的基态不仅涉及嵌套向量模式，而且还涉及许多具有与嵌套向量平行的波矢量的其他模式。有人认为，这种多模PEIERLS状态是通过使用不位于费米表面作为中间状态的电子状态的二阶嵌套过程实现的。此外，我们有……更重要的是，与单模式PEIERLS相比，在费米表面的任何一点上，电子分散剂中的任何位置的能量差距都不会消失。这些特征即使在有限温度下也可以维持，并且所有失真模式在相同的过渡时消失，温度从绝对零升高时温度也消失。过渡温度取决于电子晶格耦合常数，但不取决于失真模式。还发现这种过渡是通过声子模式的软化进行的。软化发生在过渡温度下，相关模式是带有嵌套向量的纵向和横向模式，以及与嵌套向量平行的波矢量的横向模式。在存在多模PEIERLS畸变的低温区域中，声子分散似乎取决于失真模式。由于非线性兴奋，我们仅分析了2D平方晶状体中的声学极化子。仅当电子晶体耦合常数超过临界值时，声音极化子才能稳定。如果我们通过外部电场加速极化子，则极化物的缩小程度与1D情况类似。此外，稳定极化子的速度的最大值约占声速的10％。有效的质量以及最大速度显示各向异性反映了背景晶格的平方结构。较少的