Traveling edge states in massive Dirac equations along slowly varying edges

Hu, Pipi; Xie, Ping; Zhu, Yan

doi:10.48550/arxiv.2202.13653

Cited by 4 publications

(5 citation statements)

References 41 publications

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“…We see that the bulk-boundary correspondence works well here, although the Dirac Hamiltonian is non-Hermitian. This result can be shown for more general curves using the quasiclassical approximation [49,50].…”

Section: Circular Domain Wall and Dirac Equationmentioning

confidence: 65%

Unveiling topological modes on curved surfaces

Ageev,

Iliasov

2024

Phys. Rev. B

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In this paper, we investigate topological modes of different physical systems defined on arbitrary twodimensional spatial curved surfaces. We consider the shallow water equations, inhomogeneous Maxwell's equations, and the Jackiw-Rebbi model and show how the topological protection mechanism responds to the presence of curvature in different situations. We show the existence of a line gap in the considered models and study the condition on the curve, which can host topological modes.

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Section: Circular Domain Wall and Dirac Equationmentioning

confidence: 65%

Unveiling topological modes on curved surfaces

Ageev,

Iliasov

2024

Phys. Rev. B

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“…Using ( 26) and ( 22) as well as (25), we obtain the bound for ψj given in ( 26) with j replaced by j + 1. Using (25) as well as (24), we next obtain the bound for f j+1 φ m given in (26). This allows us to construct ψ j for 0 ≤ j ≤ J to arbitrary order J provided that p 1 and p 2 are sufficiently large.…”

Section: Wavepacket Constructionmentioning

confidence: 99%

“…Wavepackets such as (2) encode this asymmetry; see [7, §1.4]. For recent analyses of relativistic modes propagating along curved domain walls, see [6,7,24]. Note that in the presence of (sufficiently highly oscillatory) perturbations of L D , the aforementioned asymmetric transport is encoded by a perturbation-dependent dispersive mode rather than the relativistic mode (2); see [8].…”

Section: Introductionmentioning

confidence: 99%

Semiclassical propagation along curved domain walls

Bal¹

2022

Preprint

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We analyze the propagation of two-dimensional dispersive and relativistic wavepackets localized in the vicinity of the zero level set Γ of a domain wall. The main applications we consider are a topologically non-trivial Dirac model and a similar but topologically trivial Klein-Gordon equation. The static domain wall models an interface separating two insulating media in possibly different topological phases. We propose a semiclassical oscillatory representation of the wavepackets and provide an estimate of their accuracy in appropriate energy norms. We describe the propagation of relativistic modes along Γ and analyze dispersive modes by a stationary phase method. In the absence of turning points, we show that arbitrary localized and smooth initial conditions may be represented as a superposition of such wavepackets. In the presence of turning points, the results apply only for sufficiently high-frequency wavepackets.

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“…the upper half-plane R × R + ). If an edge invariant emerges (typically, the signed number of gapless modes propagating along the boundary [17][18][19]), its bulk-counterpart might be obtained through bulk-edge correspondence (BEC for short, see seminal works [20,21], selected references [22][23][24] and modern review [25]).…”

Section: Introductionmentioning

confidence: 99%

Topology of 2D Dirac operators with variable mass and an application to shallow-water waves

Rossi,

Tarantola

2024

J. Phys. A: Math. Theor.

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A Dirac operator on the plane with constant (positive) mass is a Chern insulator, sitting in class D of the Kitaev table. Despite its simplicity, this system is topologically ill-behaved: the non-compact Brillouin zone prevents definition of a bulk invariant, and naively placing the model on a manifold with boundary results in violations of the bulk-edge correspondence (BEC). We overcome both issues by letting the mass spatially vary in the vertical direction, interpolating between the original model and its negative-mass counterpart. Proper bulk and edge indices can now be defined. They are shown to coincide, thereby embodying BEC. The shallow-water model exhibits the same illnesses as the 2D massive Dirac. Identical problems suggest identical solutions, and indeed extending the approach above to this setting yields proper indices and another instance of BEC.

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Traveling edge states in massive Dirac equations along slowly varying edges

Cited by 4 publications

References 41 publications

Unveiling topological modes on curved surfaces

Unveiling topological modes on curved surfaces

Semiclassical propagation along curved domain walls

Topology of 2D Dirac operators with variable mass and an application to shallow-water waves

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