发表机构
The Pennsylvania State University; University of Kentucky（宾夕法尼亚州立大学; 肯塔基大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对菱面六层层石墨烯相关体系，研究磁性维格纳晶体集体模式能否介导配对，发现其声子介导吸引力超配对阈值，可促进手性p波配对，为相关多体理论提供基础。
AI 中文摘要
近期的扫描隧道显微镜已直接成像了菱面六层层石墨烯中的电子晶体，而磁输运测量表明，在相近的载流子密度下，超导性与电荷密度波序源于同一自旋谷极化铁磁金属。受这些观测结果的启发，我们探究磁性维格纳晶体中的集体模式是否能在该场景下介导配对。我们通过研究维格纳晶体第一导带中两个电子的库珀问题来解决该问题。与常规声子介导配对不同，集体模式（玻色子）能量与单粒子（费米子）色散由电子密度控制，处于可比尺度，绝热展开无小参数。此外，由于磁性维格纳晶体不具备时间反演不变性，配对 susceptibility 中通常的库珀对数发散消失，因此吸引力必须超过有限阈值才能发生配对。这些特殊特征促使开展数值实验以探究晶体自身振动能否束缚电子。我们在哈特利-福克（Hartree–Fock）及含时哈特利-福克近似框架内得到晶体基态及其集体模式谱，并利用准玻色近似推导电子-声子哈密顿量。求解所得两电子问题后，我们发现声子介导的吸引力超过配对阈值，手性p波配对为主要不稳定性。在这些近似下，我们证明尽管时间反演对称性破缺，维格纳晶体的集体模式确实可促进手性配对。我们的结果为发展研究电子结晶与超导性的完整多体理论提供了鼓舞人心的起点。
英文摘要
Recent scanning tunneling microscopy has directly imaged electronic crystals in rhombohedral hexalayer graphene, and magnetotransport measurements suggest that superconductivity and charge-density-wave order emerge from a common spin-valley-polarized ferromagnetic metal at nearby carrier densities. Motivated by these observations, we ask whether collective modes in a magnetic Wigner crystal can mediate pairing in this setting. We address this question by studying the Cooper problem for two electrons in the first conduction band of the Wigner crystal. Unlike conventional phonon-mediated pairing, the collective mode (boson) energies and single-particle (fermion) dispersion are comparable scales controlled by the electron density, leaving no small parameter for an adiabatic expansion. Moreover, because the magnetic Wigner crystal is not time-reversal invariant, the usual Cooper logarithmic divergence in the pairing susceptibility is absent, so the attraction must exceed a finite threshold for pairing to occur. These unusual features motivate a numerical experiment to see whether the crystal's own vibrations can bind electrons. We obtain the crystalline ground state and its collective mode spectrum within Hartree--Fock and time-dependent Hartree--Fock approximation, and derive the electron--phonon Hamiltonian using the quasiboson approximation. Solving the resulting two-electron problem, we find that phonon-mediated attraction exceeds the pairing threshold, with chiral $p$-wave pairing as the leading instability. Within these approximations, we show that collective modes of a Wigner crystal can indeed favor chiral pairing despite broken time-reversal symmetry. Our results provide an encouraging starting point for developing a full many-body theory to study electronic crystallization and superconductivity.
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