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arXiv 2211.02573cond-mat.mtrl-sciquant-ph
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实际材料中的平衡态和非平衡态过屏蔽自由声子自能

Equilibrium and out-of-equilibrium over-screening free phonon self-energy in realistic materials

Andrea Marini

摘要:

在模型哈密顿中,如Fröhlich的,电子-声子相互作用被假定为从一开始就被屏蔽。当这种相互作用是通过使用最先进的密度泛函微扰理论作为出发点获得时,也会发生同样的情况。在这项工作中,我正式证明,这些方法受到严重的过度筛选错误。利用非平衡多体方法,讨论了如何将多体方法与密度泛函微扰理论相结合,以修正过屏蔽误差。通过向下折叠精确的Baym-Kadanoff方程得到了对称的静态屏蔽声子自能。这里提出的静态屏蔽近似示出具有相同的精确自能的长程空间极限,并尊重波动耗散定理。双屏蔽近似,在文献中常用的,示出,而不是被过度屏蔽,违反多体性质,并有一个错误的空间长程衰变。所提出的近似的准确性进行了测试对扩展模型的Fröhlich哈密顿的精确解,它被施加到一个典型的材料:MgB $_2$。我发现,目前的治疗提高了$57 \%$的线宽相对于什么以前已报告的异常$E_{2g}$模式。我进一步发现,$A_{2u}$模式也是异常的(它的强耦合被过度筛选的表达完全淬灭)。目前的研究结果深刻质疑基于最先进方法的方法,并影响广泛的领域,如热导率,声子不稳定性和非平衡晶格动力学。

英文摘要:

In model Hamiltonians, like Fröhlich's, the electron-phonon interaction is assumed to be screened from the beginning. The same occurs when this interaction is obtained by using the state-of-the-art density functional perturbation theory as starting point. In this work I formally demonstrate that these approaches are affected by a severe over-screening error. By using an out-of-equilibrium Many-Body technique I discuss how to merge the many-body approach with density-functional perturbation theory in order to correct the over-screening error. A symmetric statically screened phonon self-energy is obtained by down-folding the exact Baym-Kadanoff equations. The statically screened approximation proposed here is shown to have the same long-range spatial limit of the exact self-energy and to respect the fluctuation-dissipation theorem. The doubly screened approximation, commonly used in the literature, is shown, instead, to be over-screened, to violate several Many-Body properties and to have a wrong spatial long-range decay. The accuracy of the proposed approximation is tested against the exact solution of an extended model Fröhlich Hamiltonian and it is applied to a paradigmatic material: MgB$_2$. I find that the present treatment enhances the linewidths by $57 \%$ with respect to what has been previously reported for the anomalous $E_{2g}$ mode. I further discover that the $A_{2u}$ mode is also anomalous (its strong coupling being completely quenched by the over-screened expression). The present results deeply question methods based on state-of-the-art approaches and impact a wide range of fields such as thermal conductivity, phononic instabilities and non-equilibrium lattice dynamics.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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