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研究二维电子晶格系统中非线性局域激发的结构和动力学，例如一维系统中的孤子或极化子，我们必须从研究基态结构开始，这将给出令我们惊讶的是，迄今为止已知的具有半填充电子带的二维方晶格电子晶格系统中的基态并不是真正的单一基态。在我们目前的研究中，考虑了仅涉及具有嵌套矢量的畸变模式的 Peierls 模式，结果表明，真正的基态不仅涉及嵌套矢量模式，还涉及具有与嵌套矢量平行的波矢量的许多其他模式。有人认为，这种多模 Peierls 态是通过二阶嵌套过程实现的，该过程使用不位于费米表面上的电子态作为中间态。此外，我们发现存在许多非等效畸变模式，它们给出了相同的基础。国家能源和与单模 Peierls 相相比，电子色散中的能隙在费米表面上的任何点都不会消失，即使在有限温度下，这些特征也能保持，并且所有畸变模式在相同的转变温度下消失。从绝对零开始增加。转变温度取决于电子晶格耦合常数，但与畸变模式无关。这种转变还伴随着声子模式的软化，并且相关模式是在转变温度处发生的。纵向和具有嵌套矢量的横向模式和具有平行于嵌套矢量的波矢量的横向模式在存在多模 Peierls 畸变的低温区域中，声子色散似乎依赖于畸变模式。对于非线性激励，我们已经进行了分析。只有二维方晶格中的声极化子只有当电子晶格耦合常数超过临界值时才稳定。如果我们通过外部电场加速极化子，则其程度。极化子的收缩与一维情况类似。此外，稳定极化子的速度有一个最大值，约为声速的 10%，有效质量和最大速度表现出各向异性，反映了极化子的方形结构。背景格子少。