标题： 具有可调手性的多层石墨烯超导体家族：贝里环火锻造出的动量空间涡旋 显示英文标题

标题： Family of Multilayer Graphene Superconductors with Tunable Chirality: Momentum-Space Vortices Forged in the Berry-Ring of Fire

摘要： 最近，关于菱方堆叠多层石墨烯异质结构的实验报告了手性超导性的特征，这些特征源自自旋和谷极化的正常态，并且打破了时间反演对称性以及相关的反常霍尔效应。 这些发现聚焦于电子布洛赫波函数和量子几何张量在决定超导配对通道中的作用。 在这项工作中，我们研究了一个模型中具有增强的贝里曲率分布的$N$层菱方石墨烯的超导失稳现象，该分布位于动量空间中的扩展环$-$上，我们将其称为“贝里火环”$-$。在存在各向同性吸引相互作用的情况下，其空间范围可以通过参数控制。 我们确定局部相互作用在奇数$N$层系统中有利于序参量相位的$N$倍缠绕，在偶数$N$层系统中需要扩展的吸引力范围来实现配对。 对于通用的相互作用长度，我们发现了一组手性超导体，并且令人惊讶的是，在贝里火环上形成了动量空间涡旋。 这些涡旋的存在可以追溯到涉及贝里曲率的动量空间通量量子化条件，其相位缠绕由贝里通量和一个“统计通量”的组合决定，以强制执行费米-狄拉克统计。 这种序参量结构允许通过改变电子密度或位移场，在各种手性超导相之间进行原位调节的可能性。 我们讨论了如何通过实验测试这些预测，并可能在未来设备中加以利用。 显示英文摘要

摘要： Recent experiments in rhombohedrally-stacked multilayer graphene heterostructures have reported signatures of chiral superconductivity, emerging from a spin and valley-polarized normal state with broken time-reversal symmetry and an associated anomalous Hall effect. These findings bring into focus the role of the electronic Bloch wavefunction and the quantum geometric tensor in determining the superconducting pairing channel. In this work, we examine superconducting instabilities of a model of $N$-layer rhombohedral graphene that possesses an enhanced Berry curvature distribution on an extended ring in momentum space $-$ that we dub the 'Berry-ring of fire' $-$ in the presence of an isotropic attractive interaction with a parametrically controlled spatial range. We determine that local interactions favor a $N$-fold winding in the order parameter phase for odd-$N$ layered systems, with even-$N$ layers requiring a spatially extended attraction range to achieve pairing. For generic interaction lengths, we discover a family of chiral superconductors and, remarkably, momentum-space vortices nucleated on the Berry-ring of fire. The existence of these vortices can be traced to a momentum-space flux quantization condition involving the Berry curvature, with the phase winding dictated by a combination of the Berry flux and a 'statistical flux' to enforce Fermi-Dirac statistics. Such an order parameter structure allows for the possibility of in-situ tuning between various chiral superconducting phases through changes in the electron density or the displacement field. We discuss ways in which these predictions can be experimentally tested and potentially exploited in future devices.