Paired states in half-filled Landau levels

Milovanović, M. V.

doi:10.1103/physrevb.95.235304

Cited by 11 publications

(13 citation statements)

References 61 publications

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“…When taking both limits into account, a mixed-state representation with considering both interlayer and intralayer correlations has been intensively studied [11,12,28,42,64]. Such mixed representation leads to a p-wave interlayer pairing phase [11,12] or the superfluid disordering phase [42] in the intermediate distance, which are consistent with numerical finding of the incompressibility in charge channel and the disappearance of Goldstone mode as the lowest energy excitation [64].…”

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confidence: 53%

Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances

Zhu

2017

Phys. Rev. Lett.

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We study the phase diagram of quantum Hall bilayer systems with total filing νT = 1/2 + 1/2 of the lowest Landau level as a function of layer distances d. Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small d, a composite Fermi liquid at large d, and an intermediate phase for 1.1 < d/lB < 1.8 (lB is the magnetic length). The transition from the exciton superfluid to the intermediate phase is identified by (i) a dramatic change in the Berry curvature of the ground state under twisted boundary conditions on the two layers; (ii) an energy level crossing of the first excited state. The transition from the intermediate phase to the composite Fermi liquid is identified by the vanishing of the exciton superfluid stiffness. Furthermore, from our finite-size study, the energy cost of transferring one electron between the layers shows an even-odd effect and possibly extrapolates to a finite value in the thermodynamic limit, indicating the enhanced intralayer correlation. Our identification of an intermediate phase and its distinctive features shed new light on the theoretical understanding of the quantum Hall bilayer system at total filling νT = 1. Introduction.-The multilayer quantum Hall systems demonstrate tremendously rich physics when tuning the interlayer interaction by changing layer distance d. One of the prominent examples is the bilayer systems[1-4] at a total filling ν T = 1 (ν = 1/2 in each layer) with negligible tunneling. Experimentally, the bilayer systems can be realized in single wide quantum wells, double quantum wells or bilayer graphenes [5][6][7][8][9]. Theoretically, the quantum states in small and large d limits have been well understood. When the layer distance is small, the strong interlayer coulomb interaction drives the electron system into a pseudospin (layer) ferromagnetic long range order (FMLRO) state with the spontaneous interlayer phase coherence and interlayer superfluidity [10][11][12][13][14]. The FMLRO can also be described as an exciton condensation state as an electron in an orbit of one layer is always bound to a hole in another layer forming an exciton pair. This excitonic superfluid state can be described by Haplerin "111 state" wavefunction [15,16]. In the limit of infinite layer separation, the bilayer system reduces to two decoupled composite Fermi liquids (CFL) [17][18][19][20][21].

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Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances

Zhu

2017

Phys. Rev. Lett.

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“…It was also argued, analytically, in Ref. [32] that a PH-Pfaffian state, when projected into a single Landau level, must necessarily be gapless, but we have not been able to completely follow the logic behind those arguments.…”

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confidence: 76%

Topological order from disorder and the quantized Hall thermal metal: Possible applications to the ν=5/2 state

2018

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Although numerical studies modeling the quantum hall effect at filling fraction 5/2 predict either the Pfaffian (Pf) or its particle hole conjugate, the anti-Pfaffian (aPf) state, recent experiments appear to favor a quantized thermal hall conductivity with quantum number K = 5/2 , rather than the value K = 7/2 or K = 3/2 expected for the Pf or aPF state, respectively. While a particle hole symmetric topological order (the PH-Pfaffian) would be consistent with the experiments, this state is believed to be energetically unfavorable in a homogenous system. Here we study the effects of disorder that are assumed to locally nucleate domains of Pf and aPf. When the disorder is relatively weak and the size of domains is relatively large, we find that when the electrical Hall conductance is on the quantized plateau with σxy = (5/2)(e 2 /h), the value of K can be only 7/2 or 3/2, with a possible first-order-like transition between them as the magnetic field is varied. However, for sufficiently strong disorder an intermediate state might appear, which we analyze within a network model of the domain walls. Predominantly, we find a thermal metal phase, where K varies continuously and the longitudinal thermal conductivity is non-zero, while the electrical Hall conductivity remains quantized at (5/2)e 2 /h. However, in a restricted parameter range we find a thermal insulator with K = 5/2, a disorder stabilized phase which is adiabatically connected to the PH-Pfaffian. We discuss a possible scenario to rationalize these special values of parameters.

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“…On the basis of the same theory (A) the criticality of the PH Pfaffian (reversed chirality p-wave) for the zero Dirac mass case (i.e. in the presence of the PH symmetry) was predicted [14,9], that is numerically supported (no clear gapped arXiv:1908.03412v1 [cond-mat.str-el]…”

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Model interactions for Pfaffian paired states based on Chern-Simons field theory description

Đurđević

Milovanović

2019

Phys. Rev. B

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On the basis of Chern-Simons field-theoretical description we propose a simple method for derivation of model interactions for Pfaffian paired states. We verify the method in the case of Pfaffian (i.e. Moore -Read) state, and derive a general form of the model interaction in the case of PH Pfaffian. More than one Landau level is needed to establish the correlations of the PH Pfaffian, and we present the values of relevant three-body pseudo-potentials for two Landau levels. I. INTRODUCTIONThe discovery of the fractional quantum Hall effect (FQHE) at even-denominator, 5/2, filling factor [1] initiated an intensive search for viable paired states for the explanation of the effect. A new paradigm of Pfaffian paired states (with p-wave Cooper pairs) was introduced [2] that was the most important building block for the proposals of topological superconductivity and topological quantum computing. Still, after so many years of intensive experimental and theoretical research, we are not sure which paired state can be associated with the observed even-denominator FQHE. A paired state, more precisely the theoretical concept of so-called PH Pfaffian, seems according to the recent experiment [3] and other experimental data and theory [4], and theoretical proposals [4][5][6][7], closest to the solution of the puzzle at 5/2.The PH Pfaffian topological phase may be a result of a disorder dominated physics [5-8], but might be also a result of Landau level (LL) mixing in a system that may be considered uniform [8,9]. It is desirable to understand whether the PH Pfaffian (state) can be supported in a uniform system, as it was done and demonstrated in numerical experiments for Pfaffian and its particle-hole (PH) conjugated partner, anti-Pfaffian [10,11], on the basis of their model interactions. The search was proven difficult, because it was found in numerical experiments [12] that the projection of what is believed to be, an appropriate model wave-function of PH Pfaffian, to a fixed LL, represents a gapless state (not a gapped one necessary for FQHE). Therefore, for numerical experiments and in general, it is very desirable to find a model interaction for the uniform PH Pfaffian state, and in this work we will describe its general form.The proposal of the PH Pfaffian state is connected with the advance [13] in the effective (field-theoretical) description of the Fermi-liquid-like state of composite fermions (underlying quasiparticles) at compressible, even-denominator fractions. Namely, instead of classical composite fermions, we may use Dirac composite fermions to describe these fractions. The PH Pfaffian constitutes a p-wave pairing in the opposite sense of the direction dictated by external magnetic field that is materialized in the chiral motion of charge on the edge. The PH Pfaffian also makes the most natural (underlying s-wave) pairing of Dirac composite fermions. Thus the solution of the enigma of PH Pfaffian may help us to understand better pairing and superconductivity in Dirac systems raging from the FQHE ones to graphe...

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Paired states in half-filled Landau levels

Cited by 11 publications

References 61 publications

Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances

Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances

Topological order from disorder and the quantized Hall thermal metal: Possible applications to the ν=5/2 state

Model interactions for Pfaffian paired states based on Chern-Simons field theory description

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