Journal of Nanomaterials

Volume 2017, Article ID 5658796, 12 pages

https://doi.org/10.1155/2017/5658796

## One-Electron Conical Nanotube in External Electric and Magnetic Fields

Universidad Industrial de Santander, A. A. 678, Bucaramanga, Colombia

Correspondence should be addressed to L. F. Garcia; moc.liamg@ragqarfl

Received 11 August 2016; Accepted 23 January 2017; Published 15 February 2017

Academic Editor: Xin Zhang

Copyright © 2017 L. F. Garcia et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The effects of variation of the aperture angle on spectral and magnetic properties of one-electron nanotube of the axially symmetrical conical shape in the presence of the electric and magnetic fields have been investigated based on a numerical solution of the Schrödinger equation in the effective mass approximation. We show that the energy spectrum and the magnetic dipole moment of the structure are changed dramatically with increase of the cone’s aperture angle due to the interplay between the diamagnetic and centrifugal forces, which push the electron at opposite directions. Particularly, the energy levels close to the ground state become quasi-degenerate, owing to a change of the hidden symmetry, induced by the magnetic field in this structure, when its morphology is converted from the cylindrical type to the conical one and the Aharonov-Bohm oscillations of the ground state energy and of the magnetic dipole moment are quenched. We found additionally that any weak electric field breaks this hidden symmetry, splits quasi-degenerate state, and restores the Aharonov-Bohm oscillations.

#### 1. Introduction

One-dimensional nanostructures such as wires and tubes are object of intensive research at last decade owing to their unique applications in fabrication of nanoscale devices [1–3]. They are expected to play an important role as functional units in fabricating of optoelectronic devices with nanoscale dimensions. One of their applications is related to solar cells based on new photovoltaic technologies. As it has been recently demonstrated a very promising way to this goal gives a hybrid solar cell covered in silicon nanocones and a conductive organic polymer [4–6]. Another possible interesting route for one-dimensional nanostructure applications is designing of nanoantennas as solid-state single photon sources [7]. A strong dependence of the absorption of light on the geometry has been revealed recently by comparing the properties of the cylindrical and conical nanowires [8]. For optical properties of the wires, related to absorption and emission of the light, an important parameter is their polarizability, mainly governed by the anisotropic quantum confinement, but it also can be controlled by external electric and magnetic fields.

An important particularity of one-dimensional structures with axial symmetry is their extraordinary sensibility to external magnetic field related to the Aharonov-Bohm (AB) effect. Previously, AB effect has been studied for narrow quantum rings (QRs) with one and two electrons [9, 10] and with neutral and charged excitons [11–16].

It was shown previously that the presence of any nonuniformity [17–19] or an impurity [20] in a circular QR generates a partition of the closed paths of particles and quenching of the AB oscillations of one- and two-particle energy levels. One can expect that the similar magnetic properties but with weaker sensibility to defects could have narrow nanotubes where, unlike the QR, there are an infinite number of closed paths over the cylindrical surface that do not pass through defect location. AB oscillations in photoluminescence from charged exciton in InAs tubes with a thickness of several monolayers have been experimentally revealed recently [21].

Another source of a delicate nature of the AB effect in wide QRs is the spatial separation of closed classical paths corresponding to states with different angular momenta in the presence of the external magnetic field. The higher the magnetic field, the stronger is the separation between these paths and the weaker is the interference of the corresponding wave functions responsible for the AB effect. As a consequence, the amplitude of the AB oscillation is significant only if the ring is sufficiently narrow. On the other hand, in the limiting case of 1D ring the dephasing due to defects becomes such strong that it can suppress these oscillations completely. Therefore, a thin quantum tube could be a good alternative for observing the AB effect of one- and two-particle composite systems confined in them [21].

Recently, it has been demonstrated that microtube structures can be fabricated by using lattice-mismatched epitaxial layers that rolled up when freed from the substrate due to the built-in strain [22]. We believe that this technique also offers an opportunity to design nanotubes with variable cross-section radii, in which the spatial separation of the classical paths corresponding to the states with different angular momentum may be controlled by means of external fields. In order to check such possibility, we study in this paper the spectral properties of one-electron thin nanotube of the conical form with different aperture angles in the presence of external magnetic and electric fields applied simultaneously along the symmetry axis.

The paper is organized as follows. In the next section we consider a model of a thin one-electron nanotube of a conical form and describe the procedure of the separation of variables in the framework of the adiabatic approximation. The numerical results and the analysis of energies dependencies on the magnetic field in the zero-electric-field case are presented in Section 3. Also here we analyze similar dependencies for the magnetic dipole moment. The influence of the electric field on the AB oscillation and the nanotubes magnetic dipole moment is considered in Section 4. Finally, some conclusions are presented in Section 5.

#### 2. Theoretical Model

We consider a model of a nanotube of conical form with the geometrical parameters: the height , the thickness , the aperture angle , and the bottom and the top radii and , respectively (se Figure 1). The aperture angle is related to dimensions of the nanotube as