THERMAL-CONDUCTIVITY OF DISORDERED HARMONIC SOLIDS
THERMAL-CONDUCTIVITY OF DISORDERED HARMONIC SOLIDS
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DOI：
10.1103/physrevb.48.12581
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发表时间：
1993-11-01
影响因子：
3.7
通讯作者：
FELDMAN, JL
中科院分区：
文献类型：
--
作者：
ALLEN, PB;FELDMAN, JL
当晶体无序时，可能会达到这样一个点，即典型的声子平均自由程如此之短，以至于波长和平均自由程不再是尖锐的概念，教科书中关于热导率的声子模型也就崩溃了。本文提出了无序区的另一种理论，并在随后的论文中实现了非晶硅的一个实际模型。我们的想法是，主导散射可以用一个调和哈密顿量来正确地描述，这个哈密顿量原则上可以转化为一个解耦振子的一体式问题。由此可以通过类似于Kubo-Greenwood的无序金属导电率公式来精确地计算导热系数。安德森定域化被正确地包含在这个理论中；在谐和近似下，定域态不贡献电流。所需要的是一个具有大单胞和周期性边界条件的原子模型(以避免不需要的表面效应)。模型的线性尺寸应大于主导声子的平均自由程。给出了该问题的Kubo公式和Kubo-Greenwood-型公式。定义了第i精确振子状态的‘’模扩散系数‘’D(I)。热量由热流算符的非对角元素携带，这些元素具有非零贡献，因为温度梯度引入了密度矩阵[a(I)(匕首)a(J)]的非零非对角元素。我们试图从物理上解释这些结果。讨论了实现这种形式主义的方案。
As a crystal is disordered, a point may be reached where the typical mean free path of phonons is so short that the wavelength and mean free path are no longer sharp concepts, and the textbook phonongas model for thermal conductivity breaks down. This paper proposes an alternate theory for the disordered regime, and the subsequent paper implements the theory for a realistic model of amorphous silicon. The idea is that the dominant scattering is correctly described by a harmonic Hamiltonian, which is, in principle, transformable into a one-body problem of decoupled oscillators. From this the thermal conductivity can be exactly calculated by an analog of the Kubo-Greenwood formula for electrical conductivity of disordered metals. Anderson localization is correctly contained in this theory; localized states contribute no currents in harmonic approximation. What is required is an atomistic model with a large unit cell and periodic boundary conditions (to avoid undesired surface effects). The linear size of the model should be larger than the mean free paths of the dominant phonons. A Kubo formula and then a Kubo-Greenwood-type formula are derived for this problem. A ''mode diffusivity'' D(i) for the ith exact oscillator state is defined. The heat is carried by off-diagonal elements of the heat current operator, which have a nonzero contribution because the temperature gradient introduces nonzero offdiagonal elements of the density matrix [a(i)(dagger)a(j)]. An effort is made to interpret these results physically. Schemes for implementing this formalism are discussed.