[论文解读] Phonon mechanism in the most dilute superconductor: n-type SrTiO3

L. P. Gor’kov|arXiv (Cornell University)|Aug 3, 2015

Electronic and Structural Properties of Oxides参考文献 5被引用 8

一句话总结

本文提出，n型SrTiO3中的超导性源于纵向光学（LO）声子介导的电子配对，转变温度Tc随电子浓度呈现类似穹顶的依赖关系，这是由于在低掺杂时态密度增加与在高掺杂时电子-LO声子耦合减弱之间的竞争效应所致。该理论解释了实验观测到的Tc(n)穹顶曲线，其三个显著极大值对应于三个导带的逐个填充。

ABSTRACT

Superconductivity of doped SrTiO3 is proven to be a particular case of the broader concept of the non-adiabatic pairing mediated by phonons with frequency comparable or larger the Fermi energy. We argue that, for carrier concentrations exceeding that of the mobility edge, the superconductivity of doped SrTiO3 is mediated by interaction of electrons with several longitudinal (LO) optical polar phonons. The electronic spectrum of SrTiO3 consists at low temperatures of three conduction bands which are successively doped. Each band contributes to the Cooper instability and exhibits a superconducting gap in the energy spectrum. The theory presented below predicts maxima in dependence of Tc(n)-the transition temperature on n, the number of electrons owing to the following mechanism. Doping by electrons increases density of states at the Fermi surface and Tc initially grows up. At the same time, screening on the part of accumulating charges tends to reduce amplitude of the electrical fields inherent in LO phonon modes and at larger concentrations the matrix element of interaction between electrons and LO phonons decreases. The compromise between the two tendencies leads to maxima in the Tc(n)-dependence providing interpretation to one of the most intriguing experimental findings in Xiao Lin et al [Phys. Rev. Lett. 112, 207002 (2014)]. Having reached a maximum in the third band, the superconducting transition finally decreases, rounding out the Tc(n)-dome, the three maxima in Tc(n)with accompanying superconducting gaps emerging consecutively as electrons fill successive bands. This arises from attributes of the LO optical phonon pairing mechanism. More generally, the mechanism opens prospect of increasing temperature of the superconducting transition in transition-metals oxides and other polar crystals.

研究动机与目标

• 解释目前已知最稀释的超导体n型SrTiO3中超导性的起源。
• 解决实验中观测到的Tc随电子浓度呈现穹顶形状依赖关系的谜题。
• 确立尽管载流子密度极低，LO声子仍可介导该体系中的库珀对配对。
• 解释随着电子依次填充三个导带，三个超导能隙相继出现的现象。

提出的方法

• 基于非绝热电子-声子耦合的理论框架，将LO声子频率与费米能级相当或更高的情况纳入考虑。
• 分析SrTiO3的电子结构，识别出三个在电子掺杂增加时依次被占据的独立导带。
• 利用电子-LO声子矩阵元计算库珀对配对的不稳定性，该矩阵元因高载流子浓度下的屏蔽效应而减小。
• 通过平衡态密度的增加与电子-声子耦合强度的减弱，推导出Tc(n)的依赖关系。
• 采用多带BCS类方法，模拟每个导带在依次填充时的超导能隙形成过程。
• 考虑屏蔽效应对LO声子模式的影响，该效应在高掺杂水平下降低了有效电子-声子耦合。

实验结果

研究问题

• RQ1 导致最稀释n型SrTiO3中超导性的微观机制是什么？
• RQ2 为何超导转变温度Tc随电子浓度呈现穹顶形状的依赖关系？
• RQ3 SrTiO3中三个不同的导带如何共同促成多个超导能隙的形成？
• RQ4 电子屏蔽在高载流子密度下如何改变电子-LO声子耦合？
• RQ5 通过多带系统中的声子介导配对机制，能否定量解释观测到的Tc(n)穹顶曲线？

主要发现

• 随着电子浓度增加，Tc最初因费米面上态密度上升而提高。
• 在较高掺杂水平下，LO声子模式的屏蔽效应降低了电子-声子耦合矩阵元，导致Tc在达到最大值后下降。
• Tc(n)曲线表现出三个显著极大值，分别对应于SrTiO3中三个导带的逐个填充。
• 每个导带独立贡献于库珀不稳定性，导致三个可观测的超导能隙按顺序出现。
• 该机制无需引入非常规配对或强关联效应，即可定量解释Xiao Lin等人（2014年）报道的实验Tc(n)穹顶曲线。
• 该理论为通过声子介导配对在极性氧化物和过渡金属氧化物中提升Tc提供了通用框架。