Topological gap states of semiconducting armchair graphene ribbons

Jeong, Y. H.; Kim, S. C.; Yang, S.-R. Eric

doi:10.1103/physrevb.91.205441

Cited by 15 publications

(30 citation statements)

References 29 publications

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“…[8][9][10][11] suggest that superpositions of Pfaffian and anti-Pfaffian states are relevant in the half-filled LL, Ref. [44] suggests that maybe the doubling of the expected ground state degeneracy, equal to 12 = 2 × 6, is not due to the symmetric and antisymmetric superpositions of Pfaffian and anti-Pfaffian states, but due to the two possibilities for anisotropic Cooper pairs. Also Ref.…”

Section: Monolayermentioning

confidence: 99%

Paired states in half-filled Landau levels

Milovanović

2017

Phys. Rev. B

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We discuss monolayer and bilayer quantum Hall systems in which each layer is a half-filled Landau level (LL) system. In the mean field approximation of the Son's formalism there is a common pairing structure that underlines the possibilities for paired ground states in both systems. We argue that the particle-hole (PH) Pfaffian state in the (particle-hole symmetric) half-filled LL of a monolayer, and analogous state in the PH symmetric bilayer (in which each layer is half-filled LL) can be considered as {\em critical states} i.e. states that cannot describe a phase under PH symmetry. We point out that the inclusion of a PH symmetry breaking (like LL mixing) may stabilize the PH Pfaffian in a monolayer. In the bilayer case, in numerical experiments on a sphere, by choosing the PH symmetric shift, we can stabilize the interlayer correlated (111) excitonic state or critical state, for any distance between the layers, but in general, with no bias, the evolution of the bilayer includes other phases.Comment: 9 pages, rewritten, published version with important conclusion

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Section: Monolayermentioning

confidence: 99%

Paired states in half-filled Landau levels

Milovanović

2017

Phys. Rev. B

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“…Besides the Pfaffian description, the FQHSs at ν = 5/2 admits other competing descriptions that are distinct from the Pfaffian. Examples are the anti-Pfaffian [63,64], the (3,3,1) Abelian state [65], a variational wave function based on an anti-symmetrized bilayer state [66], the particle-hole symmetric Pfaffian [51,67], a stripelike alternation of the Pfaffian and anti-Pfaffian [68], and other exotic states [69,70]. Numerical studies place the ν = 5/2 FQHS in the Pfaffian universality class, ensuring the paired nature of the FQHS [71][72][73][74][75][76][77][78][79][80].…”

Section: Snapshots Of Phases Of the Two-dimensional Electron Gasmentioning

confidence: 99%

Competition of Pairing and Nematicity in the Two-Dimensional Electron Gas

Schreiber

Csáthy

2020

Annu. Rev. Condens. Matter Phys.

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Due to its extremely rich phase diagram, the two-dimensional electron gas exposed to perpendicular magnetic field has been the subject of intense and sustained study. One particularly interesting problem in this system is that of the half-filled Landau level, where the Fermi sea of composite fermions, a fractional quantum Hall state arising from a pairing instability of the composite fermions, and the quantum Hall nematic were observed in the half-filled N = 0, N = 1, and N ≥ 2 Landau levels, respectively. Thus different ground states developed in different half-filled Landau levels. This situation has recently changed, when evidence for both the paired fractional quantum Hall state and the quantum Hall nematic was reported in the half-filled N = 1 Landau level. Furthermore, a direct quantum phase transition between these two ordered states was found. These results highlight an intimate connection between pairing and nematicity, a topic of current interest in several strongly correlated systems, in a well-understood and low disorder environment. arXiv:2003.09645v1 [cond-mat.str-el]

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“…For certain values of the length of the zigzag edges an excitation gap exists that are filled with topological gap states [9]. These gap states are localized on the zigzag edges [10][11][12], and their number grows with the length of the zigzag edges L zig [13].…”

Section: Introductionmentioning

confidence: 99%

Gap states and edge properties of rectangular graphene quantum dot in staggered potential

Jeong

Yang

2017

Journal of the Korean Physical Society

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We investigate edge properties of a gapful rectangular graphene quantum dot in a staggered potential. In such a system gap states with discrete and closely spaced energy levels exist that are spatially located on the left or right zigzag edge. We find that, although the bulk states outside the energy gap are nearly unaffected, spin degeneracy of each gap state is lifted by the staggered potential. We have computed the occupation numbers of spin-up and -down gap states at various values of the strength of the staggered potential. The electronic and magnetic properties of the zigzag edges depend sensitively on these numbers. We discuss the possibility of applying this system as a single electron spintronic device.

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Topological gap states of semiconducting armchair graphene ribbons

Cited by 15 publications

References 29 publications

Paired states in half-filled Landau levels

Paired states in half-filled Landau levels

Competition of Pairing and Nematicity in the Two-Dimensional Electron Gas

Gap states and edge properties of rectangular graphene quantum dot in staggered potential

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