[论文解读] Kohn-Luttinger Superconductivity and Inter-Valley Coherence in Rhombohedral Trilayer Graphene

Yi‐Zhuang You, Ashvin Vishwanath|arXiv (Cornell University)|Sep 10, 2021

Graphene research and applications被引用 7

一句话总结

本文提出，菱面体三重石墨烯中的Kohn-Luttinger超导性源于谷间相干性（IVC）和反铁磁Hund耦合，二者驱动自旋单重态 $s$-波配对，并导致 $T_c \sim \exp(-1/\sqrt{g})$ 的增强标度。该机制解释了实验中观测到的超导性与自旋-谷对称性破缺相的紧密邻近关系，以及Pauli极限行为。

ABSTRACT

Motivated by recent experiments on ABC-stacked rhombohedral trilayer graphene (RTG) which observed spin-valley symmetry-breaking and superconductivity, we study instabilities of the RTG metallic state to symmetry breaking orders. We find that interactions select the inter-valley coherent order (IVC) as the preferred ordering channel over a wide range, whose theoretically determined phase boundaries agree well with experiments on both the hole and electron doped sides. The Fermi surfaces near van Hove singularities admit partial nesting between valleys, which promotes both inter-valley superconductivity and IVC fluctuations. We investigate the interplay between these fluctuations and the Hunds (intervalley spin) interaction using a renormalization group approach. For antiferromagnetic Hund's coupling, intervalley pairing appears in the spin-singlet channel with enhanced $T_c$, that scales with the dimensionless coupling $g$ as $T_c\sim\exp(-1/\sqrt{g})$ , compared to the standard $\exp(-1/g)$ scaling. In its simplest form, this scenario assumes a sign change in the Hund's coupling on increasing hole doping. On the other hand, the calculation incorporates breaking of the independent spin rotations between valleys from the start, and strongly selects spin singlet over spin triplet pairing, and naturally occurs in proximity to the IVC, consistent with observations.

研究动机与目标

• 解释ABC堆叠的菱面体三重石墨烯（RTG）中观测到的超导性与自旋-谷对称性破缺相之间的紧密邻近关系。
• 研究范霍夫奇点和谷间嵌套在促进超导性和谷间相干（IVC）序中的作用。
• 确定Kohn-Luttinger机制在Hund耦合增强下是否能解释观测到的高 $T_c$ 自旋单重态超导性。
• 利用重整化群分析阐明为何尽管存在SO(4)对称性，自旋三重态配对仍被抑制。

提出的方法

• 使用双带有效哈密顿量，模拟在电荷中性附近RTG的低能电子结构。
• 应用动态平均场近似（RPA）识别向谷间相干（IVC）序和超导性的不稳定性。
• 采用切片重整化群（RG）方法分析相互作用的演化，特别是谷间Hund耦合 $J_H$ 的演化。
• 分析自旋单重态配对与IVC涨落之间的相互作用，重点研究 $J_H$ 如何在 $s$-波通道中诱导吸引力。
• 考虑空穴掺杂下 $J_H$ 的符号变化，该变化可实现强配对增强。
• 从一开始就显式打破谷间自旋独立旋转对称性，从而偏好自旋单重态而非三重态配对。

Figure 1: (a) Lattice structure (top view) of rhombohedral trilayer graphene. $A_{l}$ and $B_{l}$ label the sublattices of the $l$ th graphene layer. (b) Schematic phase diagram as a function of density and displacement field, obtained here using different techniques. The IVC phase boundary is set b

实验结果

研究问题

• RQ1 Kohn-Luttinger机制能否解释菱面体三重石墨烯中观测到的自旋单重态超导性？
• RQ2 为何超导性在RTG中与自旋-谷对称性破缺相紧密相邻？
• RQ3 反铁磁Hund耦合 $J_H$ 如何增强谷间 $s$-波超导性的临界温度 $T_c$？
• RQ4 尽管系统中存在SO(4)对称性，为何未观测到自旋三重态超导性？
• RQ5 范霍夫奇点附近的谷间嵌套在稳定IVC和超导序中起什么作用？

主要发现

• 在范霍夫奇点附近，谷间相干（IVC）序是主导不稳定性，其相边界与实验在空穴和电子掺杂侧的观测结果一致。
• 在范霍夫奇点处的谷间嵌套实现了谷间的部分嵌套，促进IVC和谷间超导序的形成。
• 当Hund耦合为反铁磁性（$J_H < 0$）时，谷间密度相互作用在低能下变为吸引力，从而实现自旋单重态 $s$-波配对，且 $T_c \sim \exp(-1/\sqrt{g})$ 标度显著高于标准BCS理论。
• 重整化群流放大了弱谷间Hund耦合的影响，导致自旋单重态与自旋三重态超导态之间出现显著能级分裂。
• 由于从一开始就显式打破谷间自旋独立旋转对称性，该模型自然偏好自旋单重态配对，与实验中未观测到三重态配对的结果一致。
• SC1相的Pauli极限行为由强Zeeman耦合解释，表明 $J_H$ 驱动的配对占主导地位，而非SO(4)对称相互作用。

Figure 2: (a) Density of state (DOS) v.s. the electron density $n_{e}$ , under a typical displacement field $u_{d}=30$ meV. Insets show the $K$ valley Fermi surfaces at the corresponding doping level (those at van Hove singularities are highlighted in red). (b-c) Ideal scenarios of inter-valley nest