Striped quantum Hall state in a half-filled Landau level

Wan, Xin; Yang, Kun

doi:10.1103/physrevb.93.201303

Cited by 50 publications

(63 citation statements)

References 49 publications

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“…Alternative candidate ground states for a FQHS at this filling factor are the anti-Pfaffian 53,54 , the (3,3,1) Abelian state 55 , a variational wavefunction based on an antisymmetrized bilayer state 56 , the particle-hole symmetric Pfaffian 57,58 , a stripe-like alternation of the Pfaffian and anti-Pfaffian 59 , and other exotic states 60,61 . An ongoing intense experimental effort is not yet able to unambiguously discriminate between these gapped candidate states [33][34][35][36][37][38][39] .…”

Section: Introductionmentioning

confidence: 99%

Observation of an anomalous density-dependent energy gap of the ν=5/2 fractional quantum Hall state in the low-density regime

Samkharadze¹,

Ro²,

Pfeiffer³

et al. 2017

Phys. Rev. B

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We have studied the ν = 5/2 fractional quantum Hall state in a density-tunable sample at extremely low electron densities. For the densities accessed in our experiment, the Landau level mixing parameter κ spans the 2.52 < κ < 2.82 range. In the vicinity of 5.8 × 10 10 cm −2 or κ = 2.6 an anomalously large change in the density dependence of the energy gap is observed. Possible origins of such an anomaly are discussed, including a topological phase transition in the ν = 5/2 fractional quantum Hall state.

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Section: Introductionmentioning

confidence: 99%

Observation of an anomalous density-dependent energy gap of the ν=5/2 fractional quantum Hall state in the low-density regime

Samkharadze¹,

Ro²,

Pfeiffer³

et al. 2017

Phys. Rev. B

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“…(20) or (21) likely present when considering pairing instabilities in the half-filled LL, consistent with the exact diagonalization results of Refs. [21,22]. Finally, we point out that the Dirac based microscopic wave functions of pairing instabilities have not been proposed and tested yet.…”

Section: Dirac Composite Fermion and Cooper Pairingmentioning

confidence: 99%

Pairing instabilities of Dirac composite fermions

2016

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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 (CF's). One of the main consequences is the existence of anisotropic states in single and bilayer systems, which was previously suggested in Ref. [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 addition of a particle-hole (PH) symmetry breaking mass term may evolve into rotationally symmetric states, i.e. Pfaffian states of Halperin-Lee-Read (HLR) ordinary CF's. On the basis of the Dirac formalism, we argue that in the quantum Hall bilayer at total filling one, with decreasing distance between layers weak pairing of p-wave paired CF's is gradually transformed from Dirac to ordinary, HLRlike, with concomitant decrease in the CF number. Global characterization of low-energy spectrum based on the Dirac CF's agrees well with previous calculations performed by exact diagonalization on a torus. Finally, we discuss features of Dirac formalism when applied in this context.

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“…Here we will not consider other typed paired states [17,18,20]. Non-translational invariant states with local p x ± ip y pairing were considered recently as a possible way to restore the Landau level particle-hole symmetry (broken by both the pfaffian and the anti-pfaffian paired states) [40], as well as a paired and particle-hole symmetric state driven by disorder [19]. These states have different physical properties than those of the p x + ip y PDW state we present in this paper.…”

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confidence: 99%

“…Given the strong numerical evidence for both Pfaffian and anti-Pffafian, inhomogeneous states that restore particle-hole symmetry on large scales, while breaking it at the local level, have been proposed. Two of these proposals advocate disorder as the driving mechanism [19,21], while another one [40] proposed a stripe-type state, with alternating Pfaffian and anti-Paffian stripes. One feature of both the disorder-driven states and the PH symmetric striped state is a non-quantized thermal Hall conductivity coexisting with a quantized Hall conductivity.…”

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confidence: 99%

Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids

2019

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The properties of the isotropic incompressible ν = 5/2 fractional quantum Hall (FQH) state are described by a paired state of composite fermions in zero (effective) magnetic field, with a uniform px +ipy pairing order parameter, which is a non-Abelian topological phase with chiral Majorana and charge modes at the boundary. Recent experiments suggest the existence of a proximate nematic phase at ν = 5/2. This finding motivates us to consider an inhomogeneous paired state -a px + ipy pair-density-wave (PDW) -whose melting could be the origin of the observed liquidcrystalline phases. This state can viewed as an array of domain and anti-domain walls of the px + ipy order parameter. We show that the nodes of the PDW order parameter, the location of the domain walls (and anti-domain walls) where the order parameter changes sign, support a pair of symmetry-protected counter-propagating Majorana modes. The coupling behavior of the domain wall Majorana modes crucially depends on the interplay of the Fermi energy EF and the PDW pairing energy E pdw . The analysis of this interplay yields a rich set of topological states: (1) In the weak coupling regime (EF > E pdw ), the hybridization of domain walls leads to a Majorana Fermi surface (MFS), which is protected by inversion and particle-hole symmetries.(2) As the MFS shrinks towards degenerate Dirac points, lattice effects render it unstable towards an Abelian striped phase with two co-propagating Majorana modes at the boundary. (3) An uniform component of the order parameter, which breaks inversion symmetry, gaps the MFS and causes the system to enter a non-Abelian FQH state supporting a chiral Majorana edge state. (4) In the strong coupling regime, EF < E pdw , the bulk fermionic spectrum becomes gapped; this is a trivial phase with no chiral Majorana edge states, which is in the universality class of an Abelian Halperin paired state. The pair-density-wave order state in paired FQH system provides a fertile setting to study Abelian and non-Abelian FQH phases -as well as transitions thereof -tuned by the strength of the paired liquid crystalline order.CONTENTS * These authors contributed equally to the work.

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Striped quantum Hall state in a half-filled Landau level

Cited by 50 publications

References 49 publications

Observation of an anomalous density-dependent energy gap of the ν=5/2 fractional quantum Hall state in the low-density regime

Observation of an anomalous density-dependent energy gap of the ν=5/2 fractional quantum Hall state in the low-density regime

Pairing instabilities of Dirac composite fermions

Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids

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