Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory

Kumar, Prashant; Mulligan, Michael

doi:10.1103/physrevb.98.115105

Cited by 14 publications

(22 citation statements)

References 48 publications

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“…This conclusion holds for arbitrary disorder strength provided that the condition g = 2 is satisfied. 18 To summarize this section, the ν = 1 → 0 IQHIT of electrons is encapsulated as a ν cf = −1 → 0 IQHIT of CFs. The only difference between the two representations arises in the sign of the Hall conductance at criticality.…”

Section: Motivation: Composite Fermions With Quenched Disordermentioning

confidence: 99%

Self-duality of the integer quantum Hall to insulator transition: Composite fermion description

Kumar

Kim

2019

Phys. Rev. B

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The integer quantum Hall to insulator transition (IQHIT) is a paradigmatic quantum critical point. Key aspects of this transition, however, remain mysterious, due to the simultaneous effects of quenched disorder and strong interactions. We study this transition using a composite fermion (CF) representation, which incorporates some of the effects of interactions. As we describe, the transition also marks a IQHIT of CFs: this suggests that the transition may exhibit 'self-duality'. We show the explicit equivalence of the electron and CF Lagrangians at the critical point via the corresponding non-linear sigma models, revealing the self-dual nature of the transition. We show analytically that the resistivity tensor at the critical point is ρ c xx = ρ c xy = h e 2 , which are consistent with the expectations of self-duality, and in rough agreement with experiments.

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Section: Motivation: Composite Fermions With Quenched Disordermentioning

confidence: 99%

Self-duality of the integer quantum Hall to insulator transition: Composite fermion description

Kumar

Kim

2019

Phys. Rev. B

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“…This way, much of the phenomenology of the quantum Hall effect can be captured qualitatively by composite fermion descriptions. 8 One remaining challenge, which has been the focus of a great deal of recent work, [9][10][11][12][13][14][15][16][17][18][19] amounts to determining how the constraint of particle-hole symmetry can be incorporated in composite fermion based theories. 20 In this note, we consider the observation of particlehole symmetric fractional quantum Hall states within various composite fermion descriptions.…”

Section: Introductionmentioning

confidence: 99%

Emergent reflection symmetry from nonrelativistic composite fermions

Kumar

Mulligan

2019

Phys. Rev. B

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A recent experimental study [Pan et al., arXiv: 1902.10262] has shown that fractional quantum Hall effect gaps are essentially consistent with particle-hole symmetry in the lowest Landau level. Motivated by this result, we consider a clean two dimensional electron system (2DES) from the viewpoint of composite fermion mean-field theory. In this short note, we show that while the experiment is manifestly consistent with a Dirac composite fermion theory proposed recently by Son, it can equally well be explained within the framework of non-relativistic composite fermions, first put forward by Halperin, Lee, and Read.

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“…(2), assessing its efficacy for describing gapped PH-Pfaffian topological order in the half-filled Landau level. To this end it will prove very useful to also consider a model CFL wave function based on the HLR construction [5] (also putatively able to capture some aspects of Dirac composite fermions [12][13][14][15][42][43][44]):…”

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Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian

et al. 2018

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We numerically assess model wave functions for the recently proposed particle-hole-symmetric Pfaffian ("PHPfaffian") topological order, a phase consistent with the recently reported thermal Hall conductance [M. Banerjee et al., Nature 559, 205 (2018)] at the ever enigmatic ν = 5/2 quantum Hall plateau. We find that the most natural Moore-Read-inspired trial state for the PH-Pfaffian, when projected into the lowest Landau level, exhibits a remarkable numerical similarity on accessible system sizes with the corresponding (compressible) composite Fermi liquid. Consequently, this PH-Pfaffian trial state performs reasonably well energetically in the half-filled lowest Landau level, but is likely not a good starting point for understanding the ν = 5/2 ground state. Our results suggest that the PH-Pfaffian model wave function either encodes anomalously weak p-wave pairing of composite fermions or fails to represent a gapped, incompressible phase altogether.

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Topological phase transition underpinning particle-hole symmetry in the Halperin-Lee-Read theory

Cited by 14 publications

References 48 publications

Self-duality of the integer quantum Hall to insulator transition: Composite fermion description

Self-duality of the integer quantum Hall to insulator transition: Composite fermion description

Emergent reflection symmetry from nonrelativistic composite fermions

Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian

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