Fractional defect charges in $p$-atic liquid crystals on cones

Zhang, Grace H.; Nelson, David R.

doi:10.48550/arxiv.2201.11201

Cited by 2 publications

(12 citation statements)

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“…Note that the cone apex develops an effective topological charge of −χ. This is also compatible with the recent results of [44] in finding the ground state configuration of a p-atic liquid crystal on a cone with free boundary conditions, which is equivalent to minimizing the magnitude of the effective charge at the cone apex. In particular, the minimum energy configuration considered in [44] can have some number s 0 of charge +1/p defects at the cone apex absorbed from the free outer rim.…”

Section: Ground States Of Defects On Disk and Conesupporting

confidence: 91%

“…In Sec. V, we describe defect absorption and emission at the cone apex, with transitions and flank defect positions depending intricately on the deficit angle of the cone and the defect charges, and find excellent agreement between these analytical results and numerical energy minimizations of lattice models laid down on cones with special commensurate curvatures that allow precise computations [44]. We conclude in Sec.…”

Section: Introductionmentioning

confidence: 53%

“…In Ref. [44], free boundary conditions were imposed. Here, we consider tangential boundary conditions, by which we mean that ∇γ (the gradient of the order parameter phase) is tangential to the circumference of the base of the cone.…”

Section: B Disk/conementioning

confidence: 99%

“…Tangential boundary conditions provide a much richer arena than the free boundary conditions of Ref. [44], because defects on the cone flanks can be an intrinsic part of the ground state. For a cone, substituting ϕ = −χ ln z z and Eq.…”

Section: Ground States Of Defects On Disk and Conementioning

confidence: 99%

“…The interaction between p-atic order and curved substrates has been studied in [38,41] and it has been shown that curvature gives rise to an effective topological charge density. 1 In the special case of a cone, this would correspond to negative topological charge concentrated at the apex, and a simple argument was recently presented in [44] for the case of free boundary conditions. We re-derive this induced charge result of Vitelli and Turner [41] and use it to determine the ground state defect configuration with a fixed number of +1/p defects, which appear naturally when tangential boundary conditions are imposed at the cone base.…”

Section: Introductionmentioning

confidence: 99%

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Defect absorption and emission for $p$-atic liquid crystals on cones

Vafa,

Zhang,

Nelson

2022

Preprint

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We investigate the ground state configurations of p-atic liquid crystals on fixed curved surfaces. We focus on the intrinsic geometry and show that isothermal coordinates are particularly convenient as they explicitly encode a geometric contribution to the elastic potential. In the special case of a cone with half-angle β, the apex develops an effective topological charge of −χ, where 2πχ = 2π(1−sin β) is the deficit angle of the cone, and a topological defect of charge σ behaves as if it had an effective topological charge Q eff = (σ − σ 2 /2) when interacting with the apex. The effective charge of the apex leads to defect absorption and emission at the cone apex as the deficit angle of the cone is varied.For total topological defect charge 1, e.g. imposed by tangential boundary conditions at the edge, we find that for a disk the ground state configuration consists of p defects each of charge +1/p lying equally spaced on a concentric ring of radius d = ( p−1 3p−1 )R, where R is the radius of the disk. In the case of a cone with tangential boundary conditions at the base, we find three types of ground state configurations as a function of cone angle: (1) for sharp cones, all of the +1/p defects are absorbed by the apex; (2) at intermediate cone angles, some of the +1/p defects are absorbed by the apex and the rest lie equally spaced along a concentric ring on the flank; and (3) for nearly flat cones, all of the +1/p defects lie equally spaced along a concentric ring on the flank. Here the defect positions and the absorption transitions depend intricately on p and the deficit angle which we analytically compute. We check these results with numerical simulations for a set of commensurate cone angles and find excellent agreement.

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Section: Ground States Of Defects On Disk and Conesupporting

confidence: 91%

Section: Introductionmentioning

confidence: 53%

Section: B Disk/conementioning

confidence: 99%

Section: Ground States Of Defects On Disk and Conementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Defect absorption and emission for $p$-atic liquid crystals on cones

Vafa,

Zhang,

Nelson

2022

Preprint

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Gravitational Response of Topological Quantum States of Matter

Jiang¹,

Chen²,

Biswas³

2022

Preprint

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Identifying novel topological properties of topological quantum states of matter, such as exemplified by the quantized Hall conductance, is a valuable step towards realizing materials with attractive topological attributes that guarantee their imperviousness to realistic imperfections, disorder and environmental disturbances. Is the gravitational coupling coefficient of topological quantum states of matter a promising candidate? Substantially building on well established results for quantum Hall states, herein we report that a large class of lattice topological states of matter exhibit gravitational response, i.e., charge response to spatial curvature, which is characterized by a topologically quantized coupling constant. Remarkably, the charge-gravity relationship remains linear in the curvature, up to the maximum curvature achievable on the lattice, demonstrating absence of higher order nonlinear response. Our findings facilitate articulating the physical principles underlying the topological quantization of the gravitational coupling constant, in analogy with the insights offered by the Chern number description of the quantized Hall conductance.

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Fractional defect charges in $p$-atic liquid crystals on cones

Cited by 2 publications

References 50 publications

Defect absorption and emission for $p$-atic liquid crystals on cones

Defect absorption and emission for $p$-atic liquid crystals on cones

Gravitational Response of Topological Quantum States of Matter

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