[论文解读] Electron-K-Phonon Interaction In Twisted Bilayer Graphene

Chao‐Xing Liu, Yulin Chen+2 more|arXiv (Cornell University)|Mar 27, 2023

Graphene research and applicationsMaterials Science参考文献 10被引用 3

一句话总结

本文建立了扭曲双层石墨烯（TBG）中电子-K-声子相互作用的解析理论，表明单一光学K-声子（~160 meV）通过对称性保护的配对通道介导超导电性。研究识别出一种具有最高临界温度的单重态s波层间Chern能带配对，以及一种在手征平坦能带极限下稳定的无能隙向列d波层内Chern能带配对态，通过使用拓扑重费米子映射方法，解析推导出声子介导的吸引力。

ABSTRACT

We develop an analytic theory to describe the interaction between electrons and K-phonons and study its influence on superconductivity in the bare bands of twisted bilayer graphene (TBG). We find that, due to symmetry and the two-center approximation, only one optical K-phonon (~ 160meV) of graphene is responsible for inter-valley electron-phonon interaction. This phonon has recently been found in angular-resolved photo-emission spectroscopy to be responsible for replicas of the TBG flat bands. By projecting the interaction to the TBG flat bands, we perform the full symmetry analysis of phonon-mediated attractive interaction and pairing channels in the Chern basis, and show that several channels are guaranteed to have gapless order parameters. From the linearized gap equations, we find that the highest Tc pairing induced by this phonon is a singlet gapped s-wave inter-Chern-band order parameter, followed closely by a gapless nematic d-wave intra-Chern-band order parameter. We justify these results analytically, using the topological heavy fermion mapping of TBG which has allowed us to obtain an analytic form of phonon-mediated attractive interaction and to analytically solve the linearized and T=0 gap equations. For the intra-Chern-band channel, the nematic state with nodes is shown to be stabilized in the chiral flat band limit. While the flat band Coulomb interaction can be screened sufficiently enough - around Van-Hove singularities - to allow for electron-phonon based superconductivity, it is unlikely that this effect can be maintained in the lower density of states excitation bands around the correlated insulator states.

研究动机与目标

• 理解电子-K-声子相互作用在扭曲双层石墨烯（TBG）的平坦能带中介导超导电性的机制。
• 识别由K-声子在TBG平坦能带中诱导的对称性保护配对通道。
• 确定电子-声子耦合是否能在关联绝缘体区域克服库仑排斥作用。
• 利用TBG的拓扑重费米子映射，为声子介导的吸引力提供解析解。
• 评估库仑屏蔽对范霍夫奇点附近有效相互作用强度的影响。

提出的方法

• 为TBG中的电子-声子耦合发展了一种形变势理论，聚焦于狄拉克点附近的层内相互作用。
• 采用Bistritzer-MacDonald模型描述扭曲双层石墨烯在莫尔布里渊区中的电子结构。
• 应用双中心近似和对称性分析，表明仅一种光学K-声子模式（~160 meV）对谷间散射有贡献。
• 将电子-声子相互作用投影到平坦能带，并在Chern基中进行完整的对称性分析。
• 采用线性化间隙方程和T=0的BCS理论，解析求解配对通道。
• 使用RPA屏蔽方法计算有效库仑相互作用，介电常数和屏蔽强度作为费米能级的函数进行数值评估。

Figure 1: (a) Phonon dispersion of graphene. The irreps for phonon modes at $\Gamma$ and $\mathbf{K}_{D}$ are labelled. Inset: BZ of graphene. (b) MBZ of TBG. (c) and (d) shows the momentum dependence of the normalized gap function $|\Delta_{\mathbf{k}}|$ for the inter-Chern-band $A_{1}$ singlet (or

实验结果

研究问题

• RQ1 在TBG中，哪些声子模式通过电子-声子耦合介导电子-电子吸引力？
• RQ2 K-声子在TBG平坦能带中诱导了哪些对称性保护的配对通道？
• RQ3 在强库仑排斥作用下，特别是靠近范霍夫奇点时，电子-声子耦合能否诱导超导电性？
• RQ4 库仑屏蔽如何影响平坦能带和关联绝缘体区域中的有效相互作用强度？
• RQ5 不同配对通道（包括有能隙和无能隙态）的相对稳定性和临界温度如何？

主要发现

• 由于对称性及双中心近似，仅一种光学K-声子模式（~160 meV）对谷间电子-声子耦合有贡献。
• 最高临界温度的配对是单重态s波层间Chern能带序参量，对应有能隙的超导态。
• 无能隙的向列d波层内Chern能带配对通道也得到强烈支持，并在手征平坦能带极限下稳定。
• 通过拓扑重费米子映射，解析计算出声子介导的吸引力，与数值结果高度吻合。
• 库仑屏蔽显著降低了范霍夫奇点附近的有效相互作用强度，RPA屏蔽下有效相互作用约为~0.4 meV。
• 屏蔽效应具有强烈的能量依赖性，介电常数在态密度峰值附近达到~65.4，但在关联绝缘体态附近的低态密度区域可能仍不足。

Figure 2: (A) The superconductor order parameter amplitudes $|\Delta_{\pm}|$ (red circles and blue crosses) and the ground state energy (black dots) as a function of $\mu$ . The superconducting phase has nodes in the shadowed regime. (B) and (C) show the BdG spectrum with and without nodes at $\mu=0