论文标题
从二维和三维材料中的Fröhlich电子 - phonon相互作用的统一描述
Unified ab initio description of Fröhlich electron-phonon interactions in two-dimensional and three-dimensional materials
论文作者
论文摘要
\ textIt {ab intib}近年来，包括极地耦合在内的电子 - phonon相互作用的计算已大大提高。在散装三维（3D）材料的情况下，Fröhlich电子矩阵元素现在已经充分理解了。在二维（2D）材料的情况下，包括Fröhlich耦合的标准程序是采用库仑截断，以消除2D层的周期性图像之间的人工相互作用。尽管这些技术已经确定，但尚未研究Fröhlich耦合到二维的过渡。此外，在定期超级细胞几何形状中使用标准散装形式主义描述2D系统时仍不清楚犯错。在这里，我们通过研究由2D材料和连续介质介电板的定期超级电池中的原子偶极子在周期性的超级电池中研究原子偶极子的静电电位，从而将先前的工作推广到散装材料中的\ textIt {ab intio}fröhlichelectron-phonon矩阵元素。我们获得了矩阵元素的统一表达式，当层间分离分别倾向于零或无穷大时，该矩阵元素将减少到3D和2D系统的现有公式。这种新表达式可以准确描述2D系统中的Fröhlich矩阵元素，而无需诉诸库仑截断。我们通过直接\ textIt {ab intio}单层BN和MOS $ _2 $的密度官能扰动理论计算来验证我们的方法，我们为2DRöhlich矩阵元素提供了一个简单的表达式，该表达式可用于模型Hamiltonian方法。这项工作中概述的形式主义可能会在2D和准2D材料中发现极化物，准颗粒重新规范化，运输系数和超导性的计算中的应用。
\textit{Ab initio} calculations of electron-phonon interactions including the polar Fröhlich coupling have advanced considerably in recent years. The Fröhlich electron-phonon matrix element is by now well understood in the case of bulk three-dimensional (3D) materials. In the case of two-dimensional (2D) materials, the standard procedure to include Fröhlich coupling is to employ Coulomb truncation, so as to eliminate artificial interactions between periodic images of the 2D layer. While these techniques are well established, the transition of the Fröhlich coupling from three to two dimensions has not been investigated. Furthermore, it remains unclear what error one makes when describing 2D systems using the standard bulk formalism in a periodic supercell geometry. Here, we generalize previous work on the \textit{ab initio} Fröhlich electron-phonon matrix element in bulk materials by investigating the electrostatic potential of atomic dipoles in a periodic supercell consisting of a 2D material and a continuum dielectric slab. We obtain a unified expression for the matrix element, which reduces to the existing formulas for 3D and 2D systems when the interlayer separation tends to zero or infinity, respectively. This new expression enables an accurate description of the Fröhlich matrix element in 2D systems without resorting to Coulomb truncation. We validate our approach by direct \textit{ab initio} density-functional perturbation theory calculations for monolayer BN and MoS$_2$, and we provide a simple expression for the 2D Fröhlich matrix element that can be used in model Hamiltonian approaches. The formalism outlined in this work may find applications in calculations of polarons, quasiparticle renormalization, transport coefficients, and superconductivity, in 2D and quasi-2D materials.
