[论文解读] Superconductivity and spin canting in spin-orbit proximitized rhombohedral trilayer graphene

Caitlin L. Patterson, Owen Sheekey+16 more|arXiv (Cornell University)|Aug 19, 2024

Graphene research and applicationsMaterials Science被引用 3

一句话总结

本研究表明，通过基底邻近诱导的自旋-轨道耦合可增强菱面体三重石墨烯（RTG）中的超导性，临界温度可达约300 mK——是六方氮化硼（BN）封装RTG的三倍。增强效应并非源于对称性变化，而是由自旋-轨道耦合与洪特定律相互作用竞争引发的自旋-倾斜转变所致，该结论经哈特里-福克计算与磁测量证实，将超导性与倾斜自旋序的涨落联系起来。

ABSTRACT

Graphene and transition metal dichalcogenide flat-band systems show similar phase diagrams, replete with magnetic and superconducting phases. An abiding question has been whether magnetic ordering competes with superconductivity or facilitates pairing. The advent of crystalline graphene superconductors enables a new generation of controlled experiments to probe the microscopic origin of superconductivity. For example, recent studies of Bernal bilayer graphene show a dramatic increase in the observed domain and critical temperature $T_c$ of superconducting states in the presence of enhanced spin-orbit coupling; the mechanism for this enhancement, however, remains unclear. Here, we show that introducing spin-orbit coupling in rhombohedral trilayer graphene (RTG) via substrate proximity effect generates new superconducting pockets for both electron and hole doping, with maximal $T_c\approx$ 300mK three times larger than in RTG encapsulated by hexagonal boron nitride alone. Using local magnetometry and thermodynamic compressibility measurements, we show that superconductivity straddles an apparently continuous transition between a spin-canted state with a finite in-plane magnetic moment and a state with complete spin-valley locking. This transition is reproduced in our Hartree-Fock calculations, where it is driven by the competition between spin-orbit coupling and the carrier-density-tuned Hund's interaction. Our experiment suggests that the enhancement of superconductivity by spin-orbit coupling is driven not by a change in the ground state symmetry or degeneracy but rather by a quantitative change in the canting angle. These results align with a recently proposed mechanism for the enhancement of superconductivity in spin-orbit coupled rhombohedral multilayers, in which fluctuations in the spin-canting order contribute to the pairing interaction.

研究动机与目标

• 理解自旋-轨道耦合如何增强菱面体三重石墨烯（RTG）中的超导性。
• 确定磁序是否与超导配对竞争或促进。
• 研究自旋倾斜与自旋-谷锁定在介导超导配对中的作用。
• 建立自旋-轨道耦合与平坦能带RTG体系中增强的$T_c$之间微观机制的联系。

提出的方法

• 使用局域磁测量与热力学压缩率测量探测自旋与超导序参数。
• 进行哈特里-福克计算以模拟自旋-轨道耦合（$\lambda$）与洪特定律交换（$J_H$）之间的竞争。
• 应用吉纳斯堡-朗道自由能形式描述自旋倾斜与自旋-谷锁定转变。
• 将倾斜角定义为$\varphi = \arccos(\lambda / (2J_H n_p))$，作为极化密度$n_p$的函数。
• 从哈特里-福克期望值中提取倾斜角$\varphi = \arctan|\langle \tau^0 s^x \rangle / \langle \tau^z s^z \rangle|$。
• 在$\Delta_1$-$n_e$空间中绘制相图，以识别自旋-谷锁定态与倾斜态之间的相变。

Figure 1: Superconductivity in WSe 2 -supported rhombohedral trilayer graphene. (a) Schematic of a RTG device encapsulated between hBN and WSe 2 flakes. (b) $n_{e}$ - and $D$ -dependent inverse compressibility ( $\kappa=\partial\mu/\partial n$ ) at $B=0$ T and $T=20$ mK for Device A1. Both the overa

实验结果

研究问题

• RQ1 基底邻近诱导的自旋-轨道耦合如何影响菱面体三重石墨烯中的超导性？
• RQ2 超导临界温度$T_c$的增强是源于对称性变化，还是自旋序的定量改变？
• RQ3 自旋倾斜在自旋-轨道耦合RTG中如何介导超导配对？
• RQ4 自旋-轨道耦合与洪特定律相互作用的竞争如何调控自旋-谷锁定态与倾斜磁态之间的转变？
• RQ5 所观测到的超导性是否与自旋倾斜序参数的涨落相关？

主要发现

• 自旋-轨道邻近RTG中的超导性达到最大临界温度$T_c \approx 300$ mK，是BN封装RTG的三倍。
• 超导相与自旋倾斜态（具有面内磁矩）和自旋-谷锁定态之间的连续转变共存。
• 自旋倾斜转变由自旋-轨道耦合（$\lambda$）与洪特定律交换（$J_H$）的竞争驱动，倾斜角$\varphi = \arccos(\lambda / (2J_H n_p))$决定了磁序。
• 哈特里-福克模拟再现了实验观测到的相图，证实当$n_p \sim \lambda / J_H$时自旋倾斜现象出现。
• 超导性的增强并非源于基态对称性或简并度的变化，而是倾斜角的定量偏移所致。
• 结果支持一种近期提出的机制：自旋倾斜涨落可贡献于自旋-轨道耦合多层结构中的配对相互作用。

Figure 2: Magnetic imaging of symmetry broken states in rhombohedral trilayer graphene. (a) Magnetic signal $\delta B_{V}$ in response to a modulation of the bottom gate voltage (see Methods), plotted as a function of $n_{\textrm{e}}$ and $D$ at a single point above Device B1. (b) Same measurement a