Gauge theory of disclinations on fluctuating elastic surfaces

Abstract

A variant of a gauge theory is formulated to describe disclinations on Riemannian surfaces that may change both the Gaussian (intrinsic) and mean (extrinsic) curvatures, which implies that both internal strains and a location of the surface in R 3 may vary. Besides, originally distributed disclinations are taken into account. For the flat surface, an extended variant of the Edelen-Kadić gauge theory is obtained. Within the linear scheme our model recovers the von Karman equations for membranes, with a disclination-induced source being generated by gauge fields. For a single disclination on an arbitrary elastic surface a covariant generalization of the von Karman equations is derived.1 In particular, Σ may denote a Riemann surface, that is a 1D compact orientable complex manifold.

Electronic structure of disclinated graphene in a uniform magnetic field

“…The solution of (19), (20) for heptagonal and pentagonal defects is introduced and the local density of states is calculated here. The linear elasticity theory [14,16] is used. For the numerical calculations of LDoS, method described in [17] is exploited.…”

Electronic properties of disclinated flexible membrane beyond the inextensional limit: application to graphene

“…Under elastic deformations a surface Σ 0 evolves into some other Riemannian surface Σ, which can be thought of as a diffeomorphic map, φ : Σ 0 → Σ. Again, we find it convenient to introduce the embedding Σ → R 3 that can be realized in terms of a R 3 -valued function R i (x 1 , x 2 ), the point being that [25]…”

Dirac fermions on a disclinated flexible surface

“…The disclination defect is placed at the origin and is described by the gauge field W i=1,2 µ = 0 and W i=3 µ = W µ , where in the polar coordinates [8] W r = 0, W ϕ = ν.…”

“…In this paper, we attempt to develop a variant of the self-consistent gauge-theory approach to take into account both the smoothed apex and the topological characteristic of the defect. Actually, a part of our program was already realized in [8]. The model developed there allows us to describe disclinations on arbitrary elastic surfaces.…”

“…In general, the dynamical fields R i and W i a couple to each other. However, in the linear in elastic field approximation the gauge field can be considered as an external field [8].…”