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

本项目最初的目的是研究二维电子晶格系统中的非线性局域激发的结构和动力学，如一维系统中的孤子或极化子，如聚乙炔。我们必须从研究基态结构开始，这将为这些激发提供背景。令我们惊讶的是，目前已知的具有半填充电子带的二维方形晶格电子-晶格系统的基态并不是一个真正的基态。在早期的研究中，只考虑具有嵌套向量的畸变模态的单模佩尔斯状态。在我们目前的研究中，已经证明了真实基态不仅涉及嵌套矢量模，而且还涉及许多具有平行于嵌套矢量的波矢量的其他模。本文认为这种多模佩尔斯态是通过二阶嵌套过程实现的，这种嵌套过程使用不在费米表面上的电子态作为中间态。此外，我们还发现，在费米表面上存在许多具有相同基态能量的非等效畸变模式，并且与单模佩尔相相比，电子色散中的能隙在费米表面上的任何一点上都不会消失。这些特征即使在有限的温度下也能保持，当温度从绝对零度升高时，所有的畸变模式都在相同的转变温度下消失。转变温度与电子-晶格耦合常数有关，而与畸变模式无关。这种转变还伴随着声子模式的软化。软化发生在转变温度，对应的模态为以嵌套矢量为轴的纵模和横模，以及与嵌套矢量平行的波矢量为轴的横模。在存在多模佩尔斯畸变的低温区域，声子色散似乎依赖于畸变模式。对于非线性激励，我们只分析了二维方形晶格中的声极化子。只有当电子-晶格耦合常数超过临界值时，声极化子才稳定。如果我们用一个外电场加速极化子，极化子的范围会像一维情况一样缩小。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，反映了背景晶格的方形结构。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