Electronic properties of a graphene nanotorus under the action of external fields
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Electronic properties of a graphene nanotorus under the action of external fields Jos´e Euclides Gomes Silva a , Job Furtado, and Antonio Carlos Alonge Ramos Universidade Federal do Cariri(UFCA), Av. Tenente Raimundo Rocha, Cidade Universit´ aria, Juazeiro do Norte, Cear´ a, CEP 63048-080, Brasil
Received 1 September 2020 / Accepted 15 October 2020 Published online 7 December 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. In this paper we study the properties of an electron trapped on a torus surface. We consider the influence of surface curvature on the spectrum and the behaviour of the wave function. In addition, the effects of external electric and magnetic fields were explored. Two toroid configurations were considered, namely, a torus-like configuration and a ring-like configuration both in agreement with experimental data. We also obtain the bound states and discuss the role of geometry on the Landau levels.
1 Introduction The striking properties of two dimensional nanostructures, such as nanotubes [1], graphene [2–4] and phosphorene [5] have sparked many theoretical and experimental research. A single layer graphene exhibits no gap in the conductance band and an electron on its surface behaves as a massless particle [4]. On the other hande, a bilayer graphene possesses a quadratic dispersion relation leading to a gap in the conductance band, and interesting applications to electronics [4]. The influence of the surface geometry on the electrical properties is a topic analysed since the early days of the quantum mechanics [6–9]. By defining tangent and normal coordinates and taking the limit where the surface width vanishes, a curvature-dependent potential known as da Costa potential emerges [10,11]. This squeezing method also enables the inclusion of external fields [12], spin in a non-relativistic equation [13] and in the Dirac equation [14]. New electronic devices can be produced based on curved graphene structures. Graphene strips in a helical exhibit chiral properties [15–17] known as chiraltronics, whereas M¨obius-strip graphene behaves as topological insulator material [18]. The effects of ripples [19] and corrugated [20] surfaces upon electrons can also be described by geometric interactions. Curved graphene sheet also gives rise to effective interactions such as pseudomagnetic fields [21]. A bridge connecting two parallel layers of graphene was proposed using a nanotube [22,23] and a catenoid surface [24–26]. Another interesting geometry studied in the last years is the torus surface. In the theoretical framework, the curvature-induced bound-state eigenvalues and a
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eigenfunctions were calculated for a particle constrained to move on a torus surface considering that such particle is governed by the Schr¨odinger equation [27]. Analytical solution for the Pauli equation for a charged spin 1/2 particle moving along a toroidal surface was foun
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