论文标题
互动的狄拉克·费米斯和石墨烯中pfaffian的兴起
Interacting Dirac fermions and the rise of Pfaffians in graphene
论文作者
论文摘要
分数量子厅效应（FQHE）是一种独特的多体现象，在放置在强烈的垂直磁场中的二维电子系统中发现。这完全是由于在给定的Landau级别内的电子电子相互作用。对于Landau水平的特殊填充因子，形成了一个具有有限集体差距的多粒子不可压缩状态。在这些州中，当Landau级别填补一半时，有一个特殊的FQHE州由PFAFFIAN功能描述，该州支持遵守非亚伯统计的带电激发。这样的$ 1/2 $ -FQHE状态只能用于电子电子电位的特殊配置文件。例如，对于常规电子系统，$ 1/2 $ -FQHE状态仅发生在第二个Landau级别，而在石墨烯单层中，在任何Landau级别都找不到$ 1/2 $ -FQHE状态。低维系统的另一种类型是双层石墨烯，该石墨烯由两个石墨烯单层组成，这些单层耦合通过层间跳。该系统是准二维的，这使得通过应用与双层平行的偏置电压或平行应用的磁场来调整电子间相互作用电位。碰巧的是，在带有AB的双层石墨烯中，每个山谷有一个Landau级别，确实可以存在$ 1/2 $ -FQHE州的范围。该$ 1/2 $ -FQHE状态的性质对应用磁场具有非单调依赖性，并且比在常规电子系统中发现的磁场更稳定。
Fractional Quantum Hall effect (FQHE) is a unique many-body phenomenon, which was discovered in a two-dimensional electron system placed in a strong perpendicular magnetic field. It is entirely due to the electron-electron interactions within a given Landau level. For special filling factors of the Landau level, a many-particle incompressible state with a finite collective gap is formed. Among these states, when the Landau level is half filled, there is a special FQHE state that is described by the Pfaffian function and the state supports charged excitations that obey non-Abelian statistics. Such a $1/2$-FQHE state can be realized only for a special profile of the electron-electron potential. For example, for conventional electron systems, the $1/2$-FQHE state occurs only in the second Landau level, while in a graphene monolayer, no $1/2$-FQHE state can be found in any Landau level. Another type of low-dimensional system is the bilayer graphene, which consists of two graphene monolayers coupled through the inter-layer hopping. The system is quasi-two-dimensional, which makes it possible to tune the inter-electron interaction potential by applying either the bias voltage or the magnetic field that is applied parallel to the bilayer. It so happens that in the bilayer graphene with AB staking, there is one Landau level per valley where the $1/2$-FQHE state can indeed be present. The properties of that $1/2$-FQHE state have a nonmonotonic dependence on the applied magnetic field and this can be even more stable than the one discovered in conventional electron systems.
