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

• 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
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-14540365/
• 关键词: 2D Peierls transition; electron-lattice interaction; nesting vector; acoustic polaron; nonlinear localized excitation; phonon softening; SSH model; multimode Peierls phase; 枝分かれ構造; 2次元電子格子系; パイエルス転移; ポーラロン; バイエルス歪み; ネスティングベクトル; 金属絶縁体転移; エネル

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，这将为这种激发提供背景。令我们惊讶的是，到目前为止已知的二维方晶格电子-晶格系统中的基态并不是真正的基态。在早期的研究中，考虑了单模Peierls态，其中只包含带有嵌套矢量的畸变模。我们的研究表明，真实的基态不仅包括嵌套矢量模式，还包括许多具有平行于嵌套矢量的波矢的其他模。这种多模Peierls态是通过使用不在费米面上的电子态作为中间态的二阶嵌套过程来实现的。此外，我们还有fo…更重要的是，与单模Peierls相相反，存在许多不等价的扭曲图案，它们给出了相同的基态能量，并且电子色散中的能隙不会在费米面上的任何一点消失。这些特征即使在有限的温度下也保持不变，并且当温度从绝对零度升高时，所有的变形模都在相同的转变温度下消失。转变温度依赖于电子-晶格耦合常数，而不依赖于畸变图。这种转变还伴随着声子模的软化。软化发生在相变温度，对应的模式有嵌套矢量的纵模和横模，以及波矢平行于嵌套矢量的横模。在存在多模Peierls失真的低温区，声子色散似乎依赖于失真模式。对于非线性激发，我们只分析了2D正方形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，声极化子才是稳定的。如果我们用外加电场来加速极化子，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，反映了背景晶格的正方形结构。较少

项目成果

S.Chiba, Y.Ono: "Multi-Mode Phonon Softening in Two Dimensional Electron-Lattice System"J.Phys.Soc.Jpn.. 72(8). 1995-1999 (2003)

S.Chiba, Y.Ono：“二维电子晶格系统中的多模声子软化”J.Phys.Soc.Jpn.. 72(8)。

Y.Ono, T.Ebinuma, T.Ozawa: "Quantum Tunneling of an Acoustic Polaron in One-Dimensional Electron Lattice System"in Anderson Localization and Its Ram-ifications Disorder, Phase Coherence and Electron Correlation eds. (T.Brandes and S.Kettemann), (Springer

Y.Ono、T.Ebinuma、T.Ozawa：“一维电子晶格系统中声极化子的量子隧道”，安德森定位及其分支无序、相位相干性和电子相关编辑。

小野嘉之, 小澤利行: "Coulomb blockade effect in collision of two acoustic polarons"Physica E. 18・1-3. 358-359 (2003)

小野义之、小泽敏之：“两个声极化子碰撞中的库仑阻塞效应”Physica E. 18・1-3（2003）。

T.Ozawa, Y.Ono: "Collisions among Acoustic Polarons and Acoustic Bipolarons in One-Dimensional Electron-Lattice System"J.Phys.Soc.Jpn.. 71(6). 1518-1528 (2002)

T.Ozawa，Y.Ono：“一维电子晶格系统中声极化子和声双极化子的碰撞”J.Phys.Soc.Jpn.. 71(6)。

T.Hamano, Y.Ono: "Two-Dimensional Peierls Transition with Multimode Lattice Distortions"Physica E. (in print). (2004)

T.Hamano、Y.Ono：“具有多模晶格扭曲的二维 Peierls 转变”Physica E.（印刷中）。