论文标题
$ν= 5/2 $的反帕夫边缘模式的部分平衡
Partial equilibration of anti-Pfaffian edge modes at $ν=5/2$
论文作者
论文摘要
填充分数$ν= 5/2 $的热厅电导$ k $最近测量为$ k =2.5π^2k_b^2t/3h $ [M. Banerjee等人，自然$ {\ bf 559} $，205（2018）]。该结果的半数值（单位为$π^2k_b^2t/3h $）为存在Majorana边缘模式的存在和相应的量子Hall态托管具有非亚洲统计的准粒子提供了有力的证据。该测量是否指向pH-PFAFFIAN的实现还是反Pfaffian状态一直是辩论的主题。在这里，我们考虑了这种测量对抗Pfaffian边缘状态运输的含义。我们表明，在最低兰道水平的强库仑相互作用和近似自旋退化的极限下，反帕夫式状态允许与霍尔电导测量值一致的低温边缘阶段。这些边缘相可以在一系列温度下与部分平衡的热传输共存完整平衡的电运传输。通过对描述这些边缘状态低温电和热传输的动力学方程的研究，我们确定了参数空间的状态，控制了与实验一致的不同边缘模式之间的相互作用。
The thermal Hall conductance $K$ of the fractional quantum Hall state at filling fraction $ν=5/2$ has recently been measured to be $K=2.5 π^2k_B^2T/3h$ [M. Banerjee et al., Nature ${\bf 559}$, 205 (2018)]. The half-integer value of this result (in units of $π^2k_B^2T/3h$) provides strong evidence for the presence of a Majorana edge mode and a corresponding quantum Hall state hosting quasiparticles with non-Abelian statistics. Whether this measurement points to the realization of the PH-Pfaffian or the anti-Pfaffian state has been the subject of debate. Here we consider the implications of this measurement for anti-Pfaffian edge-state transport. We show that in the limit of a strong Coulomb interaction and an approximate spin degeneracy in the lowest Landau level, the anti-Pfaffian state admits low-temperature edge phases that are consistent with the Hall conductance measurements. These edge phases can exhibit fully-equilibrated electrical transport coexisting with partially-equilibrated heat transport over a range of temperatures. Through a study of the kinetic equations describing low-temperature electrical and heat transport of these edge states, we determine regimes of parameter space, controlling the interactions between the different edge modes, that agree with experiment.
