凝聚态中若干非线性现象的理论研究

【作者】 田强；

【导师】 马本堃；

【作者基本信息】 北京师范大学 ， 凝聚态物理， 1998， 博士

【摘要】 本论文主要涉及凝聚态中的非线性输运方面的三个问题。 一．超晶格电子输运的研究 超晶格电子在直流外电场作用下的能谱为Wannier-Stark阶梯；理想超晶格电子在直流外电场作用下，在实空间的运动是Bloch振荡。实验表明，超晶格电子在直流电场作用下，具有负微分电导特性。本文在第二章中，用Green函数，Fokker-Planck方程和非线性薛定谔方程(NLS)对超晶格中电子能态和输运性质进行了一些研究。 1．本文在§2．2中，首先通过一个新方法建立Wannier-Stark阶梯与Bloch振荡之间的直接联系，即通过外电场作用下超晶格的量子化能级(Wannier-Stark阶梯)对应的本征波函数，写出电子波包演化的Green函数，并由此计算超晶格在外电场作用下电子几率密度随时间的演化，得到了Bloch振荡。 2．我们用Fokker-Planck方程研究了超晶格电子的准经典输运。在准动量空间写出在电场作用下超晶格电子的Fokker-Planck方程，应用Zassenhaus公式和一些算符运算技巧，成功地使Fokker-Planck方程得到求解，其结果与实验符合很好。 2．1．在弱场或强阻尼情况下为线性电导； 2．2．强场或弱阻尼情况下，呈现负微分电导现象； 2．3．随着电场进一步增强，或者阻尼进一步减小，出现电流振荡，并且振荡频率在弱阻尼极限趋于熟知的Bloch频率Ω=eFa／h。 3．在本章的最后，讨论了超晶格中畴的孤子性质。在Iizuka对周期场中孤子现象分析的基础上，我们具体分析了超晶格中的畴，得到超晶格中畴的孤子解。 二．微波场中Gunn振荡的锁频特性 Gunn效应器件已被广泛地用作微波振荡，微波放大和其他各种逻辑功能器件。由于Gunn效应是强电场中热电子的非线性输运问题，与之相关的非线性输运特性的研究，一直被人们所关注。自从1982年Gunn效应的混沌行为在更多还原

【Abstract】 Bloch oscillation has been predicted long ago. In 1969, L. Esaki and R.Tsu proposed the superlattice that would facilitate the observation of quantum mechanical properties of Bloch states in a new domain of physical scale. The narrow energy bands of superlattice make it possible for electrons to be accelerated beyond the inflection point with moderate electric fields, leading to NDC and maybe leading to localized Bloch oscillation.The transport properties of superlattices have been studied by many authors experimentally and theoretically, and the theoretical studies of NDC are mainly done by the Boltzmann equation.We analyse the transport properties by the Fokker-Planck equation (FPE), and obtain some new results. We give an analysis of the perpendicular Bloch transport of electrons in a superlattice miniband for both the steady state and the oscillation cases. We have calculated the averaged drift -velocity in a superlattice. When the momentum relaxation time τ is fixed, the steady-state drift-velocity/uniform-field characteristics exhibit the expected maximum followed by negative differential conductivity (NDC). The onset field strength for the NDC is in agreement with the experiment. When the field is large, we have obtained the relation of velocity-oscillation, and its frequency is a increasing function of the field strength. Particularly, we give a new result about the oscillation frequency as a function of momentum relaxation time t, and, as expected, the frequency is the Bloch frequency Ω when τ become infinite.The Wannier-Stark ladders are the energy spectrum of superlattice electron under a steady electric field, and the Bloch oscillation is its characteristic of motion in the real space. The relation between Wannier-Stark ladders and Bloch oscillation is discussed by Green function. They are two related properties of superlattice electrons under a steady electric field.It is well known that application of sufficiently high drift fields to n-type GaAs and a number of other compound semiconductors can give rise to a far-from-equilibrium更多还原