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

本项目的目的最初是研究2D电子晶格系统中的非线性局域激发的结构和动力学，如聚乙炔的1D系统中的孤子或极化子。我们必须从研究基态结构开始，这将为这种激发提供背景。令人惊讶的是，目前已知的具有半满电子带的二维正方晶格电子-晶格系统的基态并不是真实的基态。在早期的研究中，一个单一的模式Peierls状态只涉及与嵌套向量的失真模式被认为是。在我们目前的研究中，它已被证明，真正的基态不仅涉及嵌套矢量模式，但也有许多其他模式的波矢量平行的嵌套矢量。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，我们有FO 关于我们 与单模Peierls相相比，在Fermi表面上的任何一点上，电子色散的能隙都不为零。即使在有限的温度下，这些特征仍然保持，并且当温度从绝对零度升高时，所有的畸变模式在相同的转变温度下消失。转变温度取决于电子-晶格耦合常数，但不依赖于畸变模式。这种转变也被发现伴随着声子模式的软化。软化发生在转变温度和相关的模式是纵向和横向模式的嵌套矢量和波矢量平行于嵌套矢量的横向模式。在低温区，存在多模Peierls畸变，声子色散似乎依赖于畸变模式.对于非线性激发，我们只分析了二维正方晶格中的声学极化子.只有当电子-晶格耦合常数超过一个临界值时，声学极化子才稳定。如果我们用外电场加速极化子，极化子的范围收缩类似于一维情况。此外，稳定极化子的速度存在一个极大值，约为声速的10%。有效质量以及最大速度表现出各向异性，反映了背景晶格的正方形结构。少

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