[论文解读] Effect of van Hove singularities on high-Tc superconductivity in H3S

Wataru Sano, Takashi Koretsune+3 more|arXiv (Cornell University)|Dec 23, 2015

Inorganic Fluorides and Related Compounds被引用 7

一句话总结

本研究通过在非微扰、自洽求解Migdal-Eliashberg方程时显式引入由于范霍夫奇点（vHs）引起的能量依赖态密度（DOS），重新评估了H3S中的高Tc超导性，从而消除了对经验伪库仑势的依赖。结果表明，在250 GPa下，H3S中的vHs可将Tc提升至181 K，而恒定DOS近似则使Tc高估约60 K；同时，该研究考虑了反馈效应、零点运动和非谐性，修正了约10–30 K。

ABSTRACT

One of interesting open questions for the high transition temperature (Tc) superconductivity in sulfur hydrides is why high pressure phases of H3S have extremely high Tc's. Recently, it has been pointed out that the presence of the van Hove singularities (vHs) around the Fermi level is crucial. However, while there have been quantitative estimates of Tc based on the Migdal-Eliashberg theory, the energy dependence of the density of states (DOS) has been neglected to simplify the Eliashberg equation. In this study, we go beyond the constant DOS approximation and explicitly consider the electronic structure over 40eV around the Fermi level. In contrast with the previous conventional calculations, this approach with a sufficiently large number of Matsubara frequencies enables us to calculate Tc without introducing the empirical pseudo Coulomb potential. We show that while H3S has much higher Tc than H2S for which the vHs is absent, the constant DOS approximation employed so far seriously overestimates (underestimates) Tc by ~ 60K (~ 10K) for H3S (H2S). We then discuss the impact of the strong electron-phonon coupling on the electronic structure with and without the vHs and how it affects the superconductivity. Especially, we focus on (1) the feedback effect in the self-consistent calculation of the self-energy, (2) the effect of the energy shift due to the zero-point motion, and (3) the effect of the changes in the phonon frequencies due to strong anharmonicity. We show that the effect of (1)-(3) on Tc is about 10-30K for both H3S and H2S. Eventually, Tc is estimated to be 181K for H3S at 250GPa and 34K for H2S at 140GPa, which explains the pressure dependence of Tc observed in the experiment. In addition, we evaluate the lowest order vertex correction beyond the Migdal-Eliashberg theory and discuss the validity of the Migdal approximation for sulfur hydrides.

研究动机与目标

• 通过考察电子结构中范霍夫奇点（vHs）的作用，解决H3S与H2S之间预测Tc的差异问题。
• 克服先前H3S的Migdal-Eliashberg计算中恒定态密度（DOS）近似带来的局限性。
• 定量评估电子-声子耦合、自能反馈、零点运动和声子非谐性对Tc的影响。
• 在不依赖经验伪库仑势的前提下，提供H3S在250 GPa下的Tc估计值。
• 评估Migdal近似在硫氢化物强电子-声子耦合背景下的有效性，并包含标准Eliashberg理论之外的顶点修正。

提出的方法

• 在费米能级附近40 eV范围内，通过从第一性原理电子结构计算获得的现实能量依赖DOS，求解完整的Migdal-Eliashberg方程。
• 使用大量Matsubara频率，以精确捕捉DOS的能量依赖性，避免引入经验伪库仑势。
• 执行电子自能的自洽计算，包括强电子-声子耦合引起的反馈效应。
• 通过离子位置的位移引入零点运动效应，并通过强非谐性导致的声子频率重正化来考虑其影响。
• 应用密度泛函微扰理论（DFPT）计算电子-声子矩阵元和动力学矩阵，正确处理波函数导数。
• 评估Migdal近似之外的一阶顶点修正，以检验其在硫氢化物中的有效性。

实验结果

研究问题

• RQ1 H3S中范霍夫奇点（vHs）的存在相较于缺乏vHs的H2S，如何影响超导转变温度Tc？
• RQ2 先前研究中采用的恒定DOS近似在H3S和H2S中对Tc的高估或低估程度如何？
• RQ3 自能反馈、零点运动和声子非谐性对H3S和H2S中Tc的定量影响是什么？
• RQ4 能否在不引入经验伪库仑势的前提下，获得H3S在250 GPa下的Tc估计值？
• RQ5 在硫氢化物中强电子-声子耦合背景下，Migdal近似在多大程度上是有效的？

主要发现

• 由于范霍夫奇点引起的能量依赖DOS的引入，使H3S在250 GPa下的预测Tc提高至181 K，解决了与实验观测的差异。
• 恒定DOS近似使H3S的Tc高估约60 K，使H2S的Tc低估约10 K，表明先前计算存在显著误差。
• 自洽反馈效应、零点运动和声子非谐性共同对H3S和H2S的Tc贡献了10–30 K，其中对电子-声子耦合强度的影响最大。
• 在140 GPa下，H2S的Tc估计为34 K，与实验中Tc随压力的变化趋势一致。
• Migdal-Eliashberg理论之外的一阶顶点修正较小，支持了在硫氢化物中Migdal近似的有效性。
• 本研究表明，H3S中的vHs是实现高Tc超导性的主导因素，而电子-声子耦合与自洽效应虽为次要因素，但不可忽略。