We study Cooper pairing in the Dirac composite fermion (CF) system. The presence of the mass term in the Dirac CF description (which may simulate Landau level mixing) i.e. breaking of particle-hole (PH) symmetry in this system, is a necessary condition for the existence of a PH Pfaffian-like topological state. In the scope of RPA approximation and hydrodynamic approach, we find some signatures of pairing at finite frequencies. Motivated by this insight, we extend our analysis to the case of a different but still Dirac quasi-particle (CF) representation, appropriate in the presence of a mass term, and discuss the likelihood of PH Pfaffian pairing and Pfaffian pairing in general. On the basis of gauge field effects, we find for small Dirac mass anti-Pfaffian or Pfaffian instability depending on the sign of mass, while for large mass (Landau level mixing), irrespective of its sign, PH Pfaffian-like instability.
In this review the physics of Pfaffian paired states, in the context of fractional quantum Hall effect, is discussed using field-theoretical approaches. The Pfaffian states are prime examples of topological ($p$-wave) Cooper pairing and are characterized by non-Abelian statistics of their quasiparticles. Here we focus on conditions for their realization and competition among them at half-integer filling factors. Using the Dirac composite fermion description, in the presence of a mass term, we study the influence of Landau level mixing in selecting a particular Pfaffian state. While Pfaffian an…
We introduce a family of paired-composite-fermion trial wave functions for any odd Cooper-pair angular momentum. These wave functions are parameter-free and can be efficiently projected into the lowest Landau level. We use large-scale Monte Carlo simulations to study three cases: Firstly, the Moore-Read phase, which serves us as a benchmark. Secondly, we explore the pairing associated with the anti-Pfaffian and the particle-hole-symmetric Pfaffian. Specifically, we assess whether their trial states feature exponentially decaying correlations and thus represent gapped phases of matter. For Moor…
Experimental observation of the crystallization of a paired holon state
利用紫外共振喇曼散射，在201 meV处观察到掺杂空穴梯形铜酸盐Sr $_{14}$ Cu $_{24}$ O $_{41}$的一个新的激发.的激发被发现是电荷的性质，与温度无关的激发能，并可以通过内的阶梯对断裂过程中理解。的强度密切跟踪阶梯（CDW $_L$）中的电荷密度波的顺序参数，但持续高于CDW $_L$转变温度（$T_{CDW_L}$），表明强的本地配对以上$T_{CDW_L}$。201 meV激发消失在La $_{6}$ Ca $_{8}$ Cu $_{24}$ O $_{41+δ}$和La $_{5}$ Ca $_{9}$ Cu $_{24}$ O $_{41}$中，它们是在梯中没有孔的样品。我们的研究结果表明，掺杂的空穴在梯子的复合玻色子组成的成对的holon，低于$T_{CDW}$。
Composite Fermions and the First-Landau-Level Fine Structure of the Fractional Quantum Hall Effect
采用一组标量运算符来生成两个层次状态的显式表示（例如，系列馅料1/3、2/5、3/7、.）及其结合物（填充物1、2/3、3/5、.）作为非相互作用的准电子填充FLL内的精细结构子壳层。对于平面和球形几何形状，这产生了在强度为B的磁场中填充p/（2 p +1）的不可压缩FLL状态的准电子表示，其在代数上等同于在强度为B/（2 p +1）的磁场中填充p的IQHE状态。这种结构提供了准电子/复合费米子的精确定义，它在某些方面不同于通常的描述：它们是L，Lz的本征态;它们和它们占据的FLL子壳层带有与标量对破缺有关的第三个指数I;它们在内部波函数中吸收一个而不是两个单位的磁通量;并且它们具有共同的简单结构，作为产生电子的旋量和产生磁通量的旋量的矢量积。我们认为，这些属性是由标度不变的库仑势的FLL内的非相互作用的电子的简并打破的后果。我们讨论的意义上的波函数建设支持复合费米子和分层描述的的ECOHE的基本思想。我们描述了对称性的准电子在半填充，深费米海的准电子的形式，和准电子采取马约拉纳和伪狄拉克字符。最后，我们表明，波函数可以被看作是玻色子半填充壳的费米激发，产生在半填充的运营商，不同的，但发挥相同的作用，作为Pfavian。
