位移场稳定Bernal堆叠双层石墨烯$\mathcal{N}{=}2$朗道能级中的偶分母与部分子分数量子霍尔态
Displacement field stabilizes even-denominator and partonic fractional quantum Hall states in the $\mathcal{N}{=}2$ Landau levels of Bernal-stacked bilayer graphene
- Institute of Mathematical Sciences（数学科学研究所）
- Homi Bhabha National Institute（霍米·巴巴国立学院）
- Department of Physics, Indian Institute of Technology Bombay（印度理工学院孟买分校物理系）
- Theoretical Physics Division, Physical Research Laboratory（物理研究实验室理论物理部）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
通过热力学能量计算，研究Bernal堆叠双层石墨烯$\mathcal{N}{=}2$朗道能级半填充处位移场对偶分母分数量子霍尔态的稳定作用，发现位移场软化短程排斥作用，使Moore-Read态胜出，并揭示部分子态在特定填充因子下的出现。
AI中文摘要：
Bernal堆叠双层石墨烯（BLG）中，一层石墨烯堆叠在另一层之上并横向移动一个晶格常数，在施加磁场和位移场时，其单粒子态具有显著的可调性。得益于这种可调性，近期在垂直磁场和有限层间位移场存在下的输运和扫描隧道显微镜实验，在BLG的第一激发朗道能级（即$\mathcal{N}{=}2$ LL）的半填充处观测到了偶分母分数量子霍尔（FQH）态。相比之下，在零位移场下，$\mathcal{N}{=}2$ LL的半填充处实现的是无能隙复合费米子费米液体（CFFL）。受这些实验启发，我们通过计算CFFL与Moore-Read态（一种候选的偶分母FQH态）在此设置下的热力学能量，研究二者之间的竞争，计算了BLG半填充$\mathcal{N}{=}2$ LL中随位移场变化的相图。我们发现，随着位移场增加，单粒子态变化所诱导的修正有效库仑相互作用，在短距离上软化了电子间排斥作用，从而在BLG的$\mathcal{N}{=}2$ LL中使Moore-Read态相对于CFFL得以稳定。我们还研究了BLG的$\mathcal{N}{=}2$ LL中填充因子为$2/5$、$3/7$、$4/9$和$6/13$的FQH态的性质。我们的结果表明，随着位移场增加，$3/7$、$4/9$和$6/13$处的Jain复合费米子态转变为具有不同拓扑序的态，这些态能被部分子波函数很好地描述。
英文摘要：
Bernal-stacked bilayer graphene (BLG), in which a graphene layer is stacked atop another and laterally shifted by a lattice constant, offers remarkable tunability in its single-particle states under applied magnetic and displacement fields. Owing to this tunability, recent transport and scanning tunneling microscopy experiments in the presence of a perpendicular magnetic field and finite interlayer displacement fields have observed even-denominator fractional quantum Hall (FQH) states at half-filling in the first excited, namely, $\mathcal{N}{=}2$, Landau level (LL) of BLG. In contrast, at zero displacement field, a gapless composite fermion Fermi liquid (CFFL) is realized at half-filling of the $\mathcal{N}{=}2$ LL. Motivated by these experiments, we compute the phase diagram as a function of the displacement field in the half-filled $\mathcal{N}{=}2$ LL of BLG by studying the competition between the CFFL and the Moore-Read state---a candidate even-denominator FQH state---by calculating their thermodynamic energies in this setting. We find that the modified effective Coulomb interaction, induced by changes in the single-particle states with increasing displacement field, softens the inter-electronic repulsion at short distances, thereby stabilizing the Moore-Read state over the CFFL in the $\mathcal{N}{=}2$ LL of BLG. We also study the nature of FQH states at fillings $2/5$, $3/7$, $4/9$, and $6/13$ in the $\mathcal{N}{=}2$ LL of BLG. Our results suggest that, with increasing displacement field, the Jain composite-fermion states at $3/7$, $4/9$, and $6/13$ transition into states with distinct topological order that are well-captured by parton wave functions.
