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arXiv 2202.10366cond-mat.str-el
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热导率与声子集体涨落非弹性散射理论

Thermal Conductivity and Theory of Inelastic Scattering of Phonons by Collective Fluctuations

Léo Mangeolle, Leon Balents, Lucile Savary

摘要:

我们研究了声子的内禀散射的一般量子自由度,即波动的“场”$Q$,它可能有完全一般的相关性,仅受幺正性和平移不变性的限制。从诱导散射率,我们得到的声子的热导率张量的后果。我们发现,最低阶的对角散射率,这决定了纵向电导率,是由两个点的相关函数的$Q$字段控制,而非对角散射率涉及的最小值的三到四个点的关联函数。我们得到这些相关性的一般和明确的形式,隔离霍尔电导率的贡献,并提供了一般的讨论对称性和平衡的影响。我们评估这些两点和四点的关联函数,从而为说明性的例子有序的二维反铁磁体的热输运。在这种情况下,$Q$场是自旋-晶格耦合产生的磁振子算符的复合。所需的积分的数值计算表明,结果满足所有必要的对称性限制,但否则会导致非零散射和霍尔效应,特别是这种机制导致可比的热霍尔电导率的反铁磁性的平面内和垂直的热流。

英文摘要:

We study the intrinsic scattering of phonons by a general quantum degree of freedom, i.e. a fluctuating "field" $Q$, which may have completely general correlations, restricted only by unitarity and translational invariance. From the induced scattering rates, we obtain the consequences on the thermal conductivity tensor of the phonons. We find that the lowest-order diagonal scattering rate, which determines the longitudinal conductivity, is controlled by two-point correlation functions of the $Q$ field, while the off-diagonal scattering rates involve a minimum of three to four point correlation functions. We obtain general and explicit forms for these correlations which isolate the contributions to the Hall conductivity, and provide a general discussion of the implications of symmetry and equilibrium. We evaluate these two- and four-point correlation functions and hence the thermal transport for the illustrative example of an ordered two dimensional antiferromagnet. In this case the $Q$ field is a composite of magnon operators arising from spin-lattice coupling. A numerical evaluation of the required integrals demonstrates that the results satisfy all the necessary symmetry restrictions but otherwise lead to non-vanishing scattering and Hall effects, and in particular that this mechanism leads to comparable thermal Hall conductivity for thermal currents within and normal to the plane of the antiferromagnetism.

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