Paradoxical extension of the edge states across the topological phase transition due to emergent approximate chiral symmetry in a quantum anomalous Hall system

Candido, Denis R.; Kharitonov, Maxim; Egues, J. Carlos; Hankiewicz, Ewelina M.

doi:10.1103/physrevb.98.161111

Cited by 21 publications

(29 citation statements)

References 17 publications

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“…[45,46]. Later it was applied to graphene [32,33] and topological insulators [31,36,47]. Here, we cast the BM hard-wall boundary condition for H in Eq. (1) in a form that explicitly shows U k and U c as…”

Section: B Hard-wall Boundary Conditionsmentioning

confidence: 99%

“…However, the k 2 Wilson's terms [24][25][26][27] are required to regularize the models for the calculation of topological invariants [8,9]. Moreover, numerical (finite differences) implementations of klinear models face the fermion doubling problem [28][29][30][31]. For finite systems (e.g., nanoribbons), the Dirac models allow for a variety of possible non-trivial boundary conditions, depending on the broken symmetry that imposes the confinement [32,33], as initially discussed by Berry & Mondragon [34].…”

Section: Introductionmentioning

confidence: 99%

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Interplay between boundary conditions and Wilson's mass in Dirac-like Hamiltonians

et al. 2019

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Dirac-like Hamiltonians, linear in momentum k, describe the low-energy physics of a large set of novel materials, including graphene, topological insulators, and Weyl Fermions. We show here that the inclusion of a minimal k 2 Wilson's mass correction improves the models and allows for systematic derivations of appropriate boundary conditions for the envelope functions on finite systems. Considering only Wilson's masses allowed by symmetry, we show that the k 2 corrections are equivalent to Berry-Mondragon's discontinuous boundary conditions. This allows for simple numerical implementations of regularized Dirac models on a lattice, while properly accounting for the desired boundary condition. We apply our results on graphene nanoribbons (zigzag and armchair), and on a PbSe monolayer (topological crystalline insulator). For graphene, we find generalized Brey-Fertig boundary conditions, which correctly describes the small gap seen on ab initio data for the metallic armchair nanoribbon. On PbSe, we show how our approach can be used to find spin-orbital coupled boundary conditions. Overall, our discussions are set on a generic model that can be easily generalized for any Dirac-like Hamiltonian. arXiv:1908.00145v1 [cond-mat.mes-hall]

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Section: B Hard-wall Boundary Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Interplay between boundary conditions and Wilson's mass in Dirac-like Hamiltonians

et al. 2019

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“…Conversely, the ones indicated by the green color are trivial edge states predicted previously in Ref. 63 . While the topological ones arise from the non-trivial topology of our system, the trivial ones appear when we confine subbands that have a strong linear dispersion 63 .…”

Section: Theoretical Resultsmentioning

confidence: 59%

“… 63 . While the topological ones arise from the non-trivial topology of our system, the trivial ones appear when we confine subbands that have a strong linear dispersion 63 . For this reason, these edge states appear due to the approximately chiral symmetry of the subbands 63 .…”

Section: Theoretical Resultsmentioning

confidence: 99%

Engineering topological phases in triple HgTe/CdTe quantum wells

Ferreira

Candido

Hernández

et al. 2022

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Quantum wells formed by layers of HgTe between Hg$$_{1-x}$$ 1 - x Cd$$_x$$ x Te barriers lead to two-dimensional (2D) topological insulators, as predicted by the BHZ model. Here, we theoretically and experimentally investigate the characteristics of triple HgTe quantum wells. We describe such heterostructure with a three dimensional $$8\times 8$$ 8 × 8 Kane model, and use its eigenstates to derive an effective 2D Hamiltonian for the system. From these we obtain a phase diagram as a function of the well and barrier widths and we identify the different topological phases composed by zero, one, two, and three sets of edge states hybridized along the quantum wells. The phase transitions are characterized by a change of the spin Chern numbers and their corresponding band inversions. Complementary, transport measurements are experimentally investigated on a sample close to the transition line between the phases with one and two sets of edges states. Accordingly, for this sample we predict a gapless spectrum with low energy bulk conduction subbands given by one parabolic and one Dirac subband, and with edge states immersed in the bulk valence subbands. Consequently, we show that under these conditions, local and non-local transport measurements are inconclusive to characterize a sole edge state conductivity due to bulk conductivity. On the other hand, Shubnikov-de Haas (SdH) oscillations show an excellent agreement with our theory. Particularly, we show that the measured SdH oscillation frequencies agrees with our model and show clear signatures of the coexistence of a parabolic and Dirac subbands.

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“…This is due to the existence of the edge state in the topologically nontrivial phase, known as the bulkedge correspondence, which may have practical applications such as in non-Abelian quantum computation [5] or spintronic devices [6]. Interestingly, edge states have also been reported in topologically trivial quantum dots and strips [7,8]. In all of those noninteracting systems, the edge state can be easily identified by solving the low energy Dirac Hamiltonian projected to real space [9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Corroborating the bulk-edge correspondence in weakly interacting one-dimensional topological insulators

et al. 2019

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We present a Green's function formalism to investigate the topological properties of weakly interacting one-dimensional topological insulators, including the bulk-edge correspondence and the quantum criticality near topological phase transitions, and using interacting Su-Schrieffer-Heeger model as an example. From the many-body spectral function, we find that closing of the bulk gap remains a defining feature even if the topological phase transition is driven by interactions. The existence of edge state in the presence of interactions can be captured by means of a T -matrix formalism combined with Dyson's equation, and the bulk-edge correspondence is shown to be satisfied even in the presence of interactions. The critical exponent of the edge state decay length is shown to be affiliated with the same universality class as the noninteracting limit. arXiv:1905.02583v1 [cond-mat.str-el]

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Paradoxical extension of the edge states across the topological phase transition due to emergent approximate chiral symmetry in a quantum anomalous Hall system

Cited by 21 publications

References 17 publications

Interplay between boundary conditions and Wilson's mass in Dirac-like Hamiltonians

Interplay between boundary conditions and Wilson's mass in Dirac-like Hamiltonians

Engineering topological phases in triple HgTe/CdTe quantum wells

Corroborating the bulk-edge correspondence in weakly interacting one-dimensional topological insulators

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