Localized electron states in elastic materials with disclinations

Abstract

In the framework of a gauge approach the problem of an electron localization in elastic materials with disclinations is investigated. The straight wedge disclinations, both topologically stable and unstable, as well as the disclination monopole, are considered. It is shown that for the topologically stable wedge, a disclination strongly localized in the core region electron states appears. For the topologically unstable negative wedge disclination and disclination monopole, the localization process is found to depend essentially on the depth of the deformation potential. The levels of localized electrons as well as the exact form of the normalized wavefunctions of the ground state are obtained numerically.

Charge Localization around Disclinations in Monolayer Graphite

“…Although the electronic properties of elastic materials containing topological defects have been widely studied since the early 50's [1,2] in the context of deformation potential theory, there has been a recent revival of interest in such problems using both gauge field theory [3,4,5] and Riemann-Cartan geometry [6,7,8]. In this work we use the latter approach to study the effects of the curvature associated with disclinations in a monolayer of graphite.…”

Thermal transport in materials with disclination dipoles and disclination loops

“…For finite WDDs, there is an additional linear parameter, which is a dipole length 2d. The analysis of equation (5) shows that the second crossover at low temperatures occurs due to appearance of two regimes of scattering: kd 1 and kd 1. Thus, for finite WDDs we can distinguish the following regimes of scattering:…”

“…Some aspects of the electron scattering due to straight wedge disclinations have been considered in [5] where a noticeable difference between the electronic properties of dislocations and disclinations was found-namely, while dislocations can grasp electrons on the localized levels in the core region, for negative disclinations only resonance-like electron states can exist. Also, the behaviour of the residual resistivity in simple metals caused by arrays of wedge disclinations was investigated in [6] (as a function of the density of defects n).…”

Gauge theory of disclinations on fluctuating elastic surfaces

“…An attempt at extending the EK gauge theory of defects to include fermionic fields has been made in [22]. As has been shown, the self-consistent gauge model allows to describe physically interesting effects: the Aharonov-Bohm-like electron scattering due to disclinations [20], an electron localization near topological defects [18,23] as well as a formation of the polaron-type states near dislocations [24]. We expect that incorporating fermions in the above-formulated theory may provide a new insight into disclination theory in a curved background in the presence of electrons and reveal some novel physical phenomena.…”

“…Introducing the Airy stress function χ( r) by σ bα =: ǫ bm ǫ αn ∂ m ∂ n χ( r), one can finally rewrite equations (23) and (24) as…”