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Pairing instabilities of Dirac composite fermions

机译:Dirac复合费米子的配对不稳定性

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Recently, a Dirac (particle-hole symmetric) description of composite fermions in the half-filled Landau level (LL) was proposed [D. T. Son, Phys. Rev. X 5, 031027 (2015)], and we study its possible consequences on BCS (Cooper) pairing of composite fermions (CFs). One of the main consequences is the existence of anisotropic states in single-layer and bilayer systems, which was previously suggested in Jeong and Park [J. S. Jeong and K. Park, Phys. Rev. B 91, 195119 (2015)]. We argue that in the half-filled LL in the single-layer case the gapped states may sustain anisotropy, because isotropic pairings may coexist with anisotropic ones. Furthermore, anisotropic pairings with the addition of a particle-hole symmetry-breaking mass term may evolve into rotationally symmetric states, i.e., Pfaffian states of Halperin-Lee-Read (HLR) ordinary CFs. On the basis of the Dirac formalism, we argue that in the quantum Hall bilayer at total filling factor 1, with decreasing distance between the layers, weak pairing of p-wave paired CFs is gradually transformed from Dirac to ordinary, HLR-like, with a concomitant decrease in the CF number. Global characterization of low-energy spectra based on the Dirac CFs agrees well with previous calculations performed by exact diagonalization on a torus. Finally, we discuss features of the Dirac formalism when applied in this context.
机译:最近,有人提出了半填充的朗道能级(LL)的复合费米子的狄拉克(粒子-孔对称)描述[D.儿子T. Rev. X 5,031027(2015)],我们研究了其对复合费米子(CFs)的BCS(Cooper)配对的可能影响。主要后果之一是单层和双层系统中存在各向异性状态,这在Jeong和Park之前曾提出过[J. S. Jeong和K. Park,物理学。 B 91,195119(2015)。我们认为在单层情况下的半填充LL中,带隙态可能会保持各向异性,因为各向同性配对可能与各向异性配对并存。此外,添加了破洞对称性的质量项的各向异性对可能演变成旋转对称状态,即Halperin-Lee-Read(HLR)普通CF的Pfaffian状态。根据狄拉克形式主义,我们认为在总填充因子为1的量子霍尔双层中,随着层间距离的减小,p波对CF的弱配对逐渐从狄拉克转变为普通的,类似于HLR的, CF数随之减少。基于Dirac CFs的低能谱的全局表征与通过对环上精确对角化进行的先前计算非常吻合。最后,我们讨论了在这种情况下应用狄拉克形式主义的特征。

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  • 来源
    《Physical review》 |2016年第11期|115304.1-115304.8|共8页
  • 作者单位

    Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia;

    Faculty of Physics, University of Belgrade, 11001 Belgrade, Serbia;

    Nordita, Center for Quantum Materials, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, 10691 Stockholm, Sweden;

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