Two-component fractional quantum Hall effect in the half-filled lowest Landau level in an asymmetric wide quantum well

Thiebaut, N.; Goerbig, M. O.; Regnault, Nicolas

doi:10.1103/physrevb.89.195421

Cited by 11 publications

(14 citation statements)

References 19 publications

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“…Numerically, we observe that for all the considered Halperin (m, m, n) states, the transfer matrix has nonzero eigenvalues between the topological sectors (a, b) and (MR) WF [55,56]. Reminiscent of the MR case [57], we see that the eight topological sectors of the Halperin 331 state can be split into four pairs as depicted in Fig.…”

Section: A Correlation Lengthmentioning

confidence: 81%

Matrix product state description of Halperin states

et al. 2018

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Many fractional quantum Hall states can be expressed as a correlator of a given conformal field theory used to describe their edge physics. As a consequence, these states admit an economical representation as an exact Matrix Product States (MPS) that was extensively studied for the systems without any spin or any other internal degrees of freedom. In that case, the correlators are built from a single electronic operator, which is primary with respect to the underlying conformal field theory. We generalize this construction to the archetype of Abelian multicomponent fractional quantum Hall wavefunctions, the Halperin states. These latest can be written as conformal blocks involving multiple electronic operators and we explicitly derive their exact MPS representation. In particular, we deal with the caveat of the full wavefunction symmetry and show that any additional SU(2) symmetry is preserved by the natural MPS truncation scheme provided by the conformal dimension. We use our method to characterize the topological order of the Halperin states by extracting the topological entanglement entropy. We also evaluate their bulk correlation length which are compared to plasma analogy arguments.

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Section: A Correlation Lengthmentioning

confidence: 81%

Matrix product state description of Halperin states

et al. 2018

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“…The 1/2 FQHE is observed in either double GaAs electron quantum wells (QWs) [7] or in wide GaAs QWs [6,[8][9][10][11][12][13][14][15][16][17][18] where the repulsion between the electrons makes the charge distribution bilayer-like; it has also been reported very recently in 2D hole systems confined to relatively wide GaAs QWs [19,20], and in bilayer graphene [21]. Although the ν = 1/2 FQHE in wide QWs might also be a Pfaffian state [22], it is more likely described by the Abelian, twocomponent, Halperin-Laughlin Ψ 331 wavefunction where the components are the two layers, or equivalently, the symmetric and antisymmetric electric subbands [23][24][25][26][27][28][29][30][31]. This state is stable when the interlayer tunneling, quantified by the symmetric-antisymmetric subband energy separation ∆ SAS , is much smaller than the intralayer Coulomb interaction energy, and the interlayer and intralayer Coulomb interaction energies are comparable.…”

Section: Introductionmentioning

confidence: 89%

“…This state is stable when the interlayer tunneling, quantified by the symmetric-antisymmetric subband energy separation ∆ SAS , is much smaller than the intralayer Coulomb interaction energy, and the interlayer and intralayer Coulomb interaction energies are comparable. The possibility of a ν = 1/2 FQHE in single-layer, onecomponent systems described by a Pfaffian wavefunction has also been suggested [22,27], but so far there have been no unambiguous experimental observations [17,28,30,31].…”

Section: Introductionmentioning

confidence: 99%

ν=1/2fractional quantum Hall effect in tilted magnetic fields

et al. 2015

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Magnetotransport measurements on two-dimensional electrons confined to wide GaAs quantum wells reveal a remarkable evolution of the ground state at filling factor ν = 1/2 as we tilt the sample in the magnetic field. Starting with a compressible state at zero tilt angle, a strong ν = 1/2 fractional quantum Hall state appears at intermediate angles. At higher angles an insulating phase surrounds this state and eventually engulfs it at the highest angles. This evolution occurs because the parallel component of the field renders the charge distribution increasingly bilayer-like. The evolution is qualitatively similar to the one seen, in the absence of parallel field, as a function of increasing the electron density in the quantum well, but there are some notable differences.

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“…Furthermore, we have checked numerically in the present study that the lowest-energy monocomponent states have indeed a pseudospin polarization in the z-direction, whereas we have shown within exact-diagonalization studies via a variational parameter that the twocomponent states occupy equally the ϕ + and ϕ − states. 29…”

Section: Wide Quantum Well Modelmentioning

confidence: 99%

Fractional quantum Hall states versus Wigner crystals in wide quantum wells in the half-filled lowest and second Landau levels

2015

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We investigate numerically different phases that can occur at half filling in the lowest and the first excited Landau levels in wide-well twodimensional electron systems exposed to a perpendicular magnetic field. Within a twocomponent model that takes into account only the two lowest electronic subbands of the quantum well, we derive a phase diagram that compares favorably with an experimental one by Shabani et al. [Phys. Rev. B 88, 245413 (2013)]. In addition to the compressible composite-fermion Fermi liquid in narrow wells with a substantial subband gap and the incompressible twocomponent (331) Halperin state, we identify in the lowest Landau level a rectangular Wigner crystal occupying the second subband. This crystal may be the origin of the experimentally observed insulating phase in the limit of wide wells and high electronic densities. In the second Landau level, the incompressible Pfaffian state, which occurs in narrow wells and large subband gaps, is also separated by an intermediate region from a large-well limit in which a similar rectangular Wigner crystal in the excited subband is the ground state, as for the lowest Landau level. However, the intermediate region is characterized by an incompressible state that consists of two four-flux Pfaffians in each of the components. B = /eB 26 nm/ B[T]. The well width can even lead to the formation of novel FQHSs, such as the ones observed at ν = 1/2 and 1/4 in the lowest LL. [18][19][20][21] The reminiscence with even-denominator states in bilayer quantum Hall systems 22 hints at a multi-component origin later confirmed theoretically both for symmetric [23][24][25][26][27] and asymmetric 28,29 quantum wells in terms of a (331) Halperin state 30 that competes with the compressible composite-fermion Fermi liquid (CFFL) 31 and, under certain circumstances, 24,25,28,32 with a Pfaffian. 5,6 Furthermore, these liquid phases compete with an insulating phase in the limit of very large well widths. 21In the present paper, we investigate the competition between quantum liquids and WCs at half filling in wide quantum wells within a twocomponent model originally proposed in Ref. 23. Within this model, only the two lowest electronic subbands, due to the well confinement potential, are taken into account whereas higher sub-arXiv:1503.09132v2 [cond-mat.mes-hall] 15 Dec 2015

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Two-component fractional quantum Hall effect in the half-filled lowest Landau level in an asymmetric wide quantum well

Cited by 11 publications

References 19 publications

Matrix product state description of Halperin states

Matrix product state description of Halperin states

ν=1/2fractional quantum Hall effect in tilted magnetic fields

Fractional quantum Hall states versus Wigner crystals in wide quantum wells in the half-filled lowest and second Landau levels

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