逃离复合费米海：石墨烯最低朗道能级半填充处的不可压缩态

中文摘要 AI 辅助

近期在单层和三层石墨烯中的实验，在与零朗道能级交叉相关的窄参数区域内，观察到了不可压缩的偶分母分数量子霍尔态。这令人惊讶，因为在半填充时，零朗道能级中的库仑相互作用预计会倾向于形成可压缩的复合费米液体。在此，我们首次对候选的不可压缩相以及能在这种朗道能级交叉附近稳定它们的微观机制进行了定量能量学研究。利用精确对角化和无限密度矩阵重整化群方法，我们首先研究了由有限层间距、晶格尺度效应和电子-声子耦合引起的对库仑相互作用的超短程修正。我们发现，足够强的吸引性短程相互作用会将复合费米液体首先驱动到弱配对的d波赝自旋单态，随后进入强配对态。然而，对这些短程修正的微观估计值太小，无法稳定任一不可压缩相。随后，我们通过随机相位近似中的屏蔽效应纳入朗道能级混合。屏蔽效应显著重塑了有效相互作用，抑制了弱配对区域，并强烈增强了强配对的趋势。对于现实的微观参数范围，强配对相在该范围的相当大一部分内得以稳定。我们的结果确定了朗道能级混合与超短程相互作用的协同作用，是实验中在单层和三层石墨烯中观察到的不可压缩态的一种合理微观机制，并指出强配对的复合费米子相是它们的候选基态。

英文摘要

Recent experiments in monolayer and trilayer graphene have observed incompressible even-denominator fractional quantum Hall states within narrow regions of parameter space associated with crossings of zeroth Landau levels. This is surprising because at half filling the Coulomb interaction in the zeroth Landau level is expected to favour a compressible composite Fermi liquid. Here we provide the first quantitative energetic study of the candidate incompressible phases and of the microscopic mechanisms that can stabilise them near such Landau-level crossings. Using exact diagonalization and infinite density-matrix renormalisation group, we first study ultra-short-range corrections to the Coulomb interaction arising from finite layer separation, lattice-scale effects, and electron-phonon coupling. We find that a sufficiently strong attractive short-range interaction drives the composite Fermi liquid first into a weakly paired \(d\)-wave pseudospin-singlet state and subsequently into a strongly paired state. However, microscopic estimates of these short-range corrections are far too small to stabilise either incompressible phase. We then incorporate Landau-level mixing through screening within the random-phase approximation. Screening substantially reshapes the effective interaction, suppresses the weak-pairing regime, and strongly enhances the tendency toward strong pairing. For a realistic range of microscopic parameters, the strongly paired phase is stabilised over a substantial fraction of that range. Our results identify the interplay of Landau-level mixing and ultra-short-range interactions as a plausible microscopic mechanism for the experimentally observed incompressible states in monolayer and trilayer graphene and point toward a strongly paired composite-fermion phase as their candidate ground state.

发表机构

• Condensed Matter Theory Center, Department of Physics, University of Maryland（马里兰大学凝聚态理论中心）

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