标题： 磁化螺旋边缘态与s波超导体的电子关联 显示英文标题

标题： Electronic correlations in magnetized helical edge states coupled to s-wave superconductors

摘要： 我们理论研究了电子-电子相互作用在耦合到s波超导体的一维磁化螺旋态中的作用。 我们考虑了一个部分混合的螺旋（超螺旋）区域，其中磁场（超导性）具有主导贡献。 使用玻色化和重整化群技术，展示了相互作用如何影响系统中的关联函数。 在部分混合的螺旋区域，我们发现超导配对促进了自旋密度波关联，而单态和三重态配对关联则被抑制，尤其是在吸引相互作用下。 相反，在超螺旋区域，微扰的Zeeman场在排斥相互作用下增强了自旋单态和自旋三重态-x配对。 我们计算了电荷密度波、自旋密度波和配对关联的对数和残留修正，揭示了短程和长程行为。 我们进一步研究了自旋输运特性，并通过重整化群分析了自旋电导率的温度和频率依赖性。 我们还分析了在Zeeman诱导和配对诱导能隙存在下的动量-自旋锁定载流子的输运，揭示了相互作用的影响以及两个能隙在螺旋系统中的相互作用。 显示英文摘要

摘要： We theoretically study the role of electron-electron interactions in one-dimensional magnetized helical states coupled to an s-wave superconductor. We consider a partially mixed helical (superhelical) regime, where the magnetic field (superconductivity) has a dominant contribution. Using bosonization and renormalization group techniques, it is shown how the interactions affect the correlation functions in the system. In the partially mixed helical regime, we find that superconducting pairing promotes spin-density-wave correlations, while singlet and triplet pairing correlations suppress, especially under attractive interactions. In contrast, in the superhelical regime, a perturbative Zeeman field enhances both spin singlet and spin triplet-x pairings under repulsive interactions. We calculate both logarithmic and residual corrections to charge-density-wave, spin-density-wave, and pairing correlations, revealing short- and long-range behaviors. We further investigate spin transport properties supplemented by a renormalization group analysis of the temperature and frequency dependence of spin conductivity. We also analyze the transport of momentum-spin-locked carriers in the presence of Zeeman-induced and pairing-induced gaps, uncovering the effect of interactions and the interplay between the two gaps in helical systems.