1 October 2001 Physics Letters A 288 (2001) 329–334 www.elsevier.com/locate/pla On the localization of electrons and holes by a disclination core C.A. de Lima Ribeiro a,b , Cláudio Furtado a , Fernando Moraes a,∗ a Laboratório de Física Teórica e Computacional, Departamento de Física, Universidade Federal de Pernambuco, 50.670-901 Recife, PE, Brazil b Departamento de Física, Universidade Estadual de Feira de Santana, Km 3, BR116-Norte, Feira de Santana, BA, Brazil Received 17 March 2001; received in revised form 26 June 2001; accepted 5 July 2001 Communicated by L.J. Sham Abstract In this work we study the localization of electrons and holes by a disclination core in the framework of the geometric theory of defects. In the model of finite disclination core we find that positive disclinations localize electrons and/or holes. We compute the Gamow factor for electrons and holes tunelling out of a disclination core.  2001 Elsevier Science B.V. All rights reserved. PACS: 04.50.+h; 04.20.-q; 03.65.Bz 1. Introduction Recent work [1] on the scattering of electrons by disclinations motivated us to study the localization of electrons and holes on a disclination core. Different from Ref. [1], which considers the problem in the framework of the gauge theory of defects in an elastic continuum, we use the geometric approach of Katanaev and Volovich [2], which translates the theory of defects in solids to the language of three-dimen- sional gravity. The theory of defects in solids is viewed as the anal- ogous of three-dimensional gravity in this approach. In this formalism the boundary conditions imposed by defects in elastic media are accounted for by non- Euclidean metrics. The theory, in the continuum limit, * Corresponding author. E-mail addresses: calr@uefs.br (C.A. de Lima Ribeiro), furtado@lftc.ufpe.br (C. Furtado), moraes@lftc.ufpe.br (F. Moraes). describes the solid by a Riemann–Cartan manifold where curvature and torsion are associated to disclina- tions and dislocations in the medium, respectively. The Burgers vector of a dislocation is associated to torsion, and the Frank angle of a disclination, to curvature. In this theory, the elastic deformations introduced in the medium by defects are incorporated into the metric of the manifold. The quantum and classical problems in the Riemann–Cartan manifold representing a crystal with a topological defect have been extensively ana- lyzed in recent years [3,4]. Also, Kawamura [5] and Bausch and co-workers [6] investigated the scattering of a single particle in dislocated media by a different approach and demonstrated that the equation that gov- erns the scattering is of Aharonov–Bohm type. Quan- tum dynamics in the presence of topological defects was investigated by several authors. The scattering of particles by defects and bound states were studied in previous works [7,8]. There, two of us studied the bound states of electrons and holes to negative discli- nations, where the disclinations were considered with- out a core structure. 0375-9601/01/$ – see front matter  2001 Elsevier Science B.V. All rights reserved. PII:S0375-9601(01)00561-8