The Read-Rezayi wave function is one of the candidates for the fractional quantum Hall effect at filling fraction $ν=2+\nicefrac{3}{5}$, and thereby also its hole conjugate at $2+\nicefrac{2}{5}$. We study a general class of "tripartite" composite fermion wave functions, which reduce to the Read-Rezayi ground state and quasiholes for appropriate quantum numbers, but also allow a construction of wave functions for quasiparticles and neutral excitations by analogy to the standard composite fermion theory. We present numerical evidence in finite systems that these trial wave functions capture well the low energy physics of a 4-body model interaction. We also compare the tripartite composite fermion wave functions with the exact Coulomb eigenstates at $2+\nicefrac{3}{5}$, and find reasonably good agreement. The ground state as well as several excited states of the 4-body interaction are seen to evolve adiabatically into the corresponding Coulomb states for N=15 particles. These results support the plausibility of the Read-Rezayi proposal for the $2+\nicefrac{2}{5}$ and $2+\nicefrac{3}{5}$ fractional quantum Hall effect. However, certain other proposals also remain viable, and further study of excitations and edge states will be necessary for a decisive establishment of the physical mechanism of these fractional quantum Hall states.
Static and Dynamic Properties of Type-II Composite Fermion Wigner Crystals
复合费米子的维格纳晶体是复杂出射粒子的强关联态，因此它的明确检测将具有重要意义。最近在填充因子ν = 1/3附近观察到的光学共振被解释为复合费米子的钉扎维格纳晶体的证据[Zhu et al.，物理修订版信函105，126803（2010）]。我们评估在微观理论的剪切模量和磁声子和磁等离激元色散的复合费米子维格纳晶体附近的填充因子1/3，2/5，和3/7。我们确定的晶相的稳定区域，也涉及到其钉扎模式的频率，相应的电子晶体附近的整数填充。这些结果与实验符合得很好，因此支持复合费米子维格纳晶体的钉扎模式为光共振的鉴定。我们的计算也带来了一些令人困惑的功能，如一个相对较小的熔化温度的复合费米子维格纳晶体，也表明更高的不对称性之间的复合费米子粒子和空穴比实验观察到的维格纳晶体。
Geometry of Compressible and Incompressible Quantum Hall States: Application to Anisotropic Composite Fermion Liquids
本文将分数量子霍尔态的几何描述推广到可压缩态。结果表明，在复合费米子费米表面的各向异性是这种内在的几何形状的直接反映。提出了一个简单的模型，该模型中的几何参数可以由包括电子质量各向异性在内的其它参数精确地求得。我们的结果与最近复合费米子费米面各向异性的测量结果[D. Kamburov，Y. Liu，M.沙耶甘湖N. Pfeiffer，K. W. West和K. W. Baldwin，Phys. Rev. Lett. 110，206801（2013）]。更广泛的影响，我们的研究结果进行了讨论。
We investigate the problem of intertwined orders in fractional Chern insulators by considering lattice fractional quantum Hall (FQH) states arising from pairing of composite fermions in the square-lattice Hofstadter model. At certain filling fractions, magnetic translation symmetry ensures the composite fermions form Fermi surfaces with multiple pockets, leading to the formation of finite-momentum Cooper pairs in the presence of attractive interactions. We obtain mean-field phase diagrams exhibiting a rich array of striped and topological phases, establishing paired lattice FQH states as an id…
Strong interactions and topology drive a wide variety of correlated ground states. Some of the most interesting of these ground states, such as fractional quantum Hall states and fractional Chern insulators, have fractionally charged quasiparticles. Correlations in these phases are captured by the binding of electrons and vortices into emergent particles called composite fermions. Composite fermion quasiparticles are randomly localized at high levels of disorder and may exhibit charge order when there is not too much disorder in the system. However, more complex correlations were predicted whe…
We study the integer quantum Hall plateau transition using composite fermion mean-field theory. We show that the topological $θ= π$ term in the associated nonlinear sigma model [P. Kumar et al., Phys. Rev. B 100, 235124 (2019)] is stable against a certain particle-hole symmetry violating perturbation, parameterized by the composite fermion effective mass. This result, which applies to both the Halperin, Lee, and Read and Dirac composite fermion theories, represents an emergent particle-hole symmetry. For a disorder ensemble without particle-hole symmetry, we find that $θ$ can vary continuously…
