原胞向晶胞几何投影：高效计算声子输运

然而，这类计算，尤其是在复杂晶体中，往往涉及到尴尬的几何形状，其中 Wigner-Seitz 单元格和第一布里渊区在笛卡尔空间中具有不规则、非直观的形状。此外，目前仍不清楚如何利用对称关系使晶格动力学计算在更大的单元格中更有效率。

来自美国橡树岭国家实验室的Xun Li等，提出了一种利用惯用晶胞内原始平移对称性（PTS）的高效动力学来研究晶格动力学和声子输运的方法。基于PTS，他们将原始到惯用单元格的动态方法应用于由非谐相互作用限制的热传输计算中。在惯用几何结构中，这种PTS动力学方法通过在典型传统动力学中隐藏的守恒规则，显著减少准粒子散射相空间，并减少散射矩阵元素计算中的求和次数，从而降低热导率计算的计算成本。

作者通过计算三种不同空间群材料的声子输运性质，证明了这种PTS方法的便利性，这三种材料为空间群R3m的GeTe、空间群I2₁3的固体N₂和空间群R-3的铁磁CrCl₃ 。作者提出的动力学方法能够准确描述传输现象，并且比传统动力学方法在计算上成本更低，这对于研究复杂材料系统中的准粒子相互作用具有重要价值。该文近期发布于npj Computational Materials 9: 193 (2023)。

Fig. 4 Thermal conductivity of N2 (black curve, inset), GeTe (blue curve), and CrCl3 (red curve) from PTS dynamics as a function of temperature in bulk naturally occurring samples.

Editorial Summary

Calculations and simulations of crystalline material properties are typically based on periodically arranged unit cells that contain the smallest number of degrees of freedom, i.e., the primitive unit cell. The most widely used primitive cells are called Wigner-Seitz cells (WSC) and their corresponding first Brillouin zones (FBZ). These are typically used for calculations of lattice vibrational and transport properties because they have the cheapest computational cost. However, such calculations, particularly in complex crystals, often have awkward geometries with WSC and FBZ having irregular, non-intuitive shapes in Cartesian space. In addition, it is not well known how to use symmetry relations to make lattice dynamical calculations more efficient in larger unit cells. 

Xun Li et al. from Oak Ridge National Laboratory, explored the lattice dynamics and phonon transport using an efficient dynamic method that utilizes primitive translational symmetry (PTS) within conventional cells. Theyapplied this primitive to conventional cell dynamic method based on PTS to thermal transport calculations limited by anharmonic interactions. In conventional geometries, this PTS dynamic method significantly reduces the computational cost of thermal conductivity calculations by reducing the quasiparticle scattering phase space through a conservation rule that is hidden in typical conventional dynamics and reducing the number of summations in scattering matrix element calculations. They demonstrated the convenience of this PTS method by calculating phonon transport properties for three materials from different space groups: GeTe with space group R3m, solid N₂ with space group I2₁3, and ferromagnetic CrCl₃ with space group R-3. The proposed dynamics accurately describes transport phenomena and costs significantly less computationally compared to conventional dynamics, which is valuable for studying quasiparticle interactions in complex material systems. This article was recently published in npj Computational Materials 9: 193 (2023).

原文Abstract及其翻译

Primitive to conventional geometry projection for efficient phonon transport calculations（有效计算声子输运的原胞到晶胞几何投影）

Xun Li, Simon Thébaud & Lucas Lindsay 

Abstract

The primitive Wigner-Seitz cell and corresponding first Brillouin zone (FBZ) are typically used in calculations of lattice vibrational and transport properties as they contain the smallest number of degrees of freedom and thus have the cheapest computational cost. However, in complex materials, the FBZ can take on irregular shapes where lattice symmetries are not apparent. Thus, conventional cells (with more atoms and regular shapes) are often used to describe materials, though dynamical and transport calculations are more expensive. Here we discuss an efficient anharmonic lattice dynamic method that maps conventional cell dynamics to primitive cell dynamics based on translational symmetries. Such symmetries have not been utilized in typical lattice dynamical calculations. This leads to phase interference conditions that act like conserved quantum numbers and a conservation rule for phonon scattering that is hidden in conventional dynamics which significantly reduces the computational cost. We demonstrate this method for phonon transport in a variety of materials with inputs from first-principles calculations and attribute its efficiency to reduced scattering phase space and fewer summations in scattering matrix element calculations.

摘要 

Wigner-Seitz原胞和相应的第一布里渊区（FBZ）通常用于计算晶格振动和输运性质，因为它们包含最小的自由度，因此计算成本也最低。然而，在复杂材料中，FBZ可能是不规则的形状，晶格对称不明显。因此，尽管其动力学计算和输运计算更昂贵，惯用晶胞（具有更多的原子和规则的形状）也经常被用来描述材料。本文讨论了一种有效的非谐晶格动力学方法，该方法利用平移对称性将惯用晶胞动力学映射到原胞动力学上。这种对称性还没有被用于典型的晶格动力学计算。这导致了类似于守恒量子数的相位干涉条件，以及隐藏在传统动力学中的声子散射守恒规则，这大大降低了计算成本。我们利用第一性原理计算的输入，演示了这种方法用于各种材料中的声子输运的计算，并将其效率归因于减少散射相空间和减少散射矩阵元计算中的求和。