【作者】 李连钢；

【导师】 阮永丰；

【作者基本信息】 天津大学 ， 材料物理与化学， 2007， 博士

【摘要】 准一维材料中电荷密度波现象是电子在强关联作用下的一种集体凝聚的表现。人们在铜氧化合物高温超导陶瓷材料以及很多其他材料中都可以发现电荷密度波的存在。电荷密度波作为一种电子集体凝聚状态,在导电特性方面,会表现出非线性电导、窄带噪声、存在非线性电导的启动阈场等现象。在电荷密度波理论研究方面, Grüner及其合作者提出所谓单粒子模型,并给出一个非线性微分方程,即Grüner方程,来描述电荷密度波的导电行为。由于Grüner方程是一个非线性微分方程,人们无法得到它的严格的解析解。Grüner等人运用过阻尼近似方法,略去方程中的二阶微分项,得到比较满意结果。但是,Grüner得到的电导公式的导数在阈场处是发散的,这与实验结果不太符合。通过分析可以看到,这种缺陷并非Grüner方程本身所造成的,是由于对方程的近似处理所造成的。本篇文章中,运用微分方程向量场理论对Grüner方程进行了定性分析,得出了在外场大于一定的阈值情况下方程将具有稳定的、唯一的周期解的结论。本文还从数学上对外场与周期解依赖关系进行了严格证明,并得出了在一定条件下,使方程具有周期解的阈值将是恒定不变的。这一结果为我们在物理上的进一步分析,提供了可靠的数学基础。在此基础上,我们可以从Grüner方程导出,单段电荷密度波在外场作用下将会产生滑移速度叠加周期变化速度的运动,周期变化速度形成窄带噪音,滑移速度形成直流电流分量,并且遵循线性的欧姆定律。我们将这些结果与Portis多分段模型相结合,提出各段电荷密度波之间“弹性串联”机制,将分段与分段之间的相互作用转化为内力处理,并指出单段CDW的周期变化速度中的直流分量将转换为分段之间的相互之间挤压或拉伸的内力而失去对电流直流分量的贡献。最终我们可以导出与Fleming经验公式完全一致结果。更多还原

【Abstract】 Charge density-waves is a type of electron collective behaviors in a condensed mode. In the CDW materials there are a lot of anomalous characters with it. Nonlinear conductivity, narrow-band noise, threshold field and so on are found by experiments. Grüner and his collaborators first proposed the single-particle model to explain them. In the model they gave a nonlinear differential equation to describing the behaviors of electronic transportation. Because this differential equation which is named as Grüner’s equation doesn’t have analytical solution, they derived the conductivity formula by over-damping approximation. Although this formula satisfied with the experiences very well in some degree, the derivative of conductivity is divergent at the threshold. This is contradictory with the result of experiment, but we think that the contradictory is due to neglecting the second order differential term of the equation.In this paper, we analyze the equation by the means of the rotating vector field theory. Using the mathematical analysis method we obtain the relation between the applied field E and the periodical solution of the equation. It is concluded that in the over-damping situation the E0 in Grüner’s equation is just the critical value of the applied field E. we also obtain a conclusion that the equation has a unique and stable periodical solution when the applied field E is large than the critical value of the applied field E. According to the conclusion, it could be naturally derived that the sliding current of a segment of charge density wave obeys the Ohm’s law. Sequentially we apply these conclusions with Portis’s multiple segment model. We put forward a idea of elastic connection accounting for the connection of different segments. The theoretical result we derive from these for describing nonlinear conductivity of charge density wave is consistent with the experiential formula given by Fleming.更多还原