Chern 带中手性超导体的分类学

中文摘要 AI 辅助

最近，在包括菱面体多层石墨烯和扭曲双层 MoTe$_2$ 在内的几种范德华系统中，观察到了手性超导电性的证据。在后者中，超导电性出现在接近分数量子 Chern 绝缘体的载流子密度处。这提出了一个问题：在具有强排斥相互作用的拓扑带中的电子系统中，可能出现哪些种类的超导体。在这里，我们采用目标相位优化方法，在 Chern 带中相互作用电子的最小模型中搜索手性超导体。我们从配对结合能的符号振荡出发，为超导体构建了一个可微的损失函数，并将基于梯度的优化与严格的筛选程序相结合，以识别和表征超导体。我们将此框架应用于具有屏蔽库仑相互作用的周期性调制 Landau 能级中的无自旋电子，通过精确对角化，揭示了一个广泛的手性超导相家族。在填充因子 $\nu=2/3$ 时，我们重现了先前确定的 $f-\mathrm{i} f$ 空穴超导体，并发现了额外的 $p\pm \mathrm{i} p$ 和 $f+\mathrm{i} f$ 电子和空穴超导体，它们出现在理想量子几何极限附近及远离该极限处。在 $\nu=1/2$ 时，我们确定了 $p- \mathrm{i} p$ 电子和 $f-\mathrm{i} f$ 空穴超导体，并首次发现了手性超导体与复合费米液体之间的直接转变。我们的结果表明，Chern 带中的手性超导电性包含一个由竞争配对不稳定性组成的多样化景观，并确立了目标相位优化作为在复杂相互作用系统中搜索量子相的一般策略。

英文摘要

Evidence for chiral superconductivity has recently been observed in several van der Waals systems including rhombohedral multilayer graphene and twisted bilayer MoTe$_2$. In the latter, superconductivity emerges at carrier densities near a fractional Chern insulator. This raises the question of what kinds of superconductors may emerge in a system of electrons in a topological band with strong repulsive interactions. Here, we adapt the target-phase optimization method to search for chiral superconductors in a minimal model of interacting electrons in a Chern band. We construct a differentiable loss function for superconductors from the sign oscillation of the pair-binding energy and combine gradient-based optimization with a rigorous screening procedure to identify and characterize superconductors. Applying this framework within exact diagonalization to spinless electrons in periodically modulated Landau levels with screened Coulomb interactions, we uncover a broad family of chiral superconducting phases. At filling $ν=2/3$, we recover the previously identified $f-\mathrm{i} f$ hole superconductors and find additional $p\pm \mathrm{i} p$ and $f+\mathrm{i} f$ superconductors of both electrons and holes, occurring near and far from the limit of ideal quantum geometry. At $ν=1/2$, we identify $p- \mathrm{i} p$ electron and $f-\mathrm{i} f$ hole superconductors and find, for the first time, a direct transition between chiral superconductors and composite Fermi liquids. Our results reveal that chiral superconductivity in Chern bands comprises a diverse landscape of competing pairing instabilities and establish target-phase optimization as a general strategy for searching for quantum phases in complex interacting systems.

发表机构

• Massachusetts Institute of Technology（麻省理工学院）
• Stanford University（斯坦福大学）

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