Elsevier

Physica B: Condensed Matter

Volume 623, 15 December 2021, 413337
Physica B: Condensed Matter

On the interaction of an electron with a nonuniform electric field under the influence of a cut-off point induced by the spiral dislocation topology

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Highlights

  • Cut-off point induced by the spiral dislocation topology.

  • Topological effects of a spiral dislocation on the spectrum of energy.

  • Absence of Aharonov–Bohm-type effect for bound states from the topology of the defect.

  • Non-null revival time associated with the radial quantum number.

Abstract

We analyse the interaction of an electron with a nonuniform electric field under the influence of a cut-off point induced by the topology of a spiral dislocation. We show that the presence of the cut-off point yields eigenvalues of energy which are infinitely degenerated. Besides, we show that the energy eigenvalues are influenced by the topology of the defect even though there is no interaction between the electron and the defect. Furthermore, we show that the influence of a cut-off point induced by the spiral dislocation topology gives rise to a non-null revival time associated with the radial quantum number.

Introduction

Recently, Edery and Audin [1] considered the interaction of an electron with a uniform magnetic field and showed that when a linear electric field is applied in the z-direction, it can modify the degeneracy of the Landau levels [2]. In another perspective, a linear electric field applied in the radial direction has been considered in studies of an electron in an elastic medium with a disclination [3] and a spiral dislocation [4]. Nonuniform electric fields are typically used in studies of neutral particle systems. Indeed, several works with neutral particle systems can be found in the literature. The most known work was made by Aharonov and Casher [5], where they showed the interaction of the permanent magnetic dipole moment of a neutral particle with the nonuniform electric field produced by a linear distribution of electric charges yields a geometric quantum phase. In this line of research, geometric quantum phases have been proposed to neutral particles with induced electric dipole moment [6], [7] and electric quadrupole moment [8]. Later, nonuniform electric fields have been proposed with the aim of achieving the Landau-type quantization for neutral particles. By considering the nonuniform electric field produced by a uniform distribution of electric charges, the Landau-type quantization was obtained for neutral particles with permanent magnetic dipole moment [9] and with induced electric dipole moment [10]. The Landau-type quantization for neutral particles has also been dealt with noncommutative coordinates [11], [12] and in rotating reference frame [13]. With the same nonuniform electric field of Refs. [9], [10], a Coulomb-type potential has been studied for an atom with magnetic quadrupole moment in Ref. [14].

In this work, we study the interaction of an electron with a linear electric field under the influence of a cut-off point that stems from the topology of a spiral dislocation. This nonuniform electric field is produced by a uniform distribution of electric charges inside a long nonconductor cylinder. Then, we show that the influence of this cut-off point modifies the spectrum of energy in contrast to that obtained in Refs. [3], [4]. Further, we discuss the influence of the spiral dislocation topology on the quantum revivals [15]. We show that a non-null revival time associated with the radial quantum number can be obtained due to the influence of this cut-off point on the interaction of the electron with the linear electric field.

The structure of this paper is: in Section 2, we show how the topology of the spiral dislocation can induce a cut-off point, and thus, we search for bound state solutions to the Schrödinger equation; in Section 3, we focus on the classical period and the revival time [15], [16], [17], [18]; in Section 4, we present our conclusions.

Section snippets

Cut-off point induced by the spiral dislocation topology

Linear topological defects, like a dislocation, can modify the electronic properties of the elastic medium. Examples of the interest in dislocations are the studies made in semiconductors [19], [20], [21] and quantum dots [22]. The most known way of describing dislocations in solids is via the Volterra process [23], [24], [25], which consists in the process of “cut” and “glue” of the elastic medium. In the Volterra process, we can find two kinds of dislocations: the screw dislocation and the

Quantum revivals

Quantum revivals appear when the wave function recovers its initial shape at a time, which is known as the revival time [15], [16], [17], [18]. Quantum revivals have been investigated in several systems, such as, the infinite square well [17], [18], [50], [51], [52], quantum pendulum [53], position-dependent mass systems [54], Rydberg atoms [55], [56], [57] and graphene [58], [59].

According to Refs. [15], [16], [60], [61], [62], when a quantum system has one quantum number ν, the energy

Conclusions

We have seen that the topological effects of the spiral dislocation can modify the spectrum of energy that stems from the interaction of an electron and an electric field produced by a uniform distribution of electric charges inside a long nonconductor cylinder [3]. This occurs due to the fact that the topology of the spiral dislocation can induce a cut-off point in the system. We have obtained the eigenvalues of energy, where each energy level is infinitely degenerated with respect to the

CRediT authorship contribution statement

A.V.D.M. Maia: Conceived the mathematical model, Interpreted the results, Writing – original draft, Made most of the calculations in consultation with K.B.. K. Bakke: Conceived the mathematical model, Interpreted the results, Writing – original draft.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgement

The authors would like to thank CNPq for financial support. All authors approved the version of the manuscript to be published.

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