Electric field-induced electronic structure and intersubband transitions of a hydrogen molecular ion in a gaussian-type quantum ring

Eur. Phys. J. Plus (2024) 139:616 https://doi.org/10.1140/epjp/s13360-024-05421-7 Regular Article Electric field-induced electronic structure and intersubband transitions of a hydrogen molecular ion in a gaussian-type quantum ring S. Sakiroglu1,a , H. Sari2 1 Physics Department, Faculty of Science, Dokuz Eylül University, 35390 Izmir, Turkey 2 Department of Mathematics and Natural Science Education, Faculty of Education, Sivas Cumhuriyet University, 58140 Sivas, Turkey Received: 28 February 2024 / Accepted: 2 July 2024 © The Author(s) 2024 Abstract In this work, the influence of an external electric field on the electronic structure and intersubband transitions of a singly ionized double-donor system in a GaAs quantum ring defined by Gaussian-type potentials is investigated theoretically. Within the framework of the effective mass approach, the two-dimensional diagonalization method is used for the solution of the Schrödinger equation to obtain the eigen energies and corresponding wave functions. Numerical results reveal that the electronic energy spectrum and the linear optical absorption coefficient of the ring are remarkably affected by the strength of the lateral electric field, internuclear distance and parameters defining the confinement potential. Also, it has been shown that beyond the anti-crossing point, the wave functions exchange their symmetries without mixing, which is a characteristic feature of energy-level anti-crossing. 1 Introduction Modern crystal growth techniques made possible the fabrication of nanometer-scale systems with various shapes and geometries [1, 2] where quantum dots (QDs) [3, 4] and quantum rings (QRs) stand as significant delegates of this class [5]. Unique and distinct optoelectronic properties of these quantum-confined nanostructures, in comparison with conventional ones, offer a remarkable improvement in the design and production of devices including solar cells, sensors, memory devices, etc. [6–8]. Doubly connected geometry of QRs provides a characteristic electronic structure, external field response and transport properties [9–11]. In this context, QRs can be regarded as meso-dimensional structures owing to their dimensionality lying between QDs and quantum wires [12, 13]. The possibility of the experimental observation of the Aharonov–Bohm (AB) and Berry phase effects, persistent currents and quantum interference phenomenon has placed these structures at the center of an intensive field of research [14–16]. In numerous works conducted on the physical characteristics of QRs, different theoretical models have been utilized to model the confinement in two- and three-dimensional (2D and 3D) quantum rings [15–17]. Simonin and coworkers theoretically studied the single-particle electron structure of self-assembled QRs. The structure is defined by two lateral confining potentials, a displaced parabola and a centrifugal-like core potential [14]. The magnetic field effects on the electronic energy spectra and optical features of QRs defined by cylindrical square-well and parabolic geometrical confinement potential models have been discussed in Ref. [17]. Magnetic field dependence of the intraband optical absorption coefficients (OACs) of the 2D QR modeled with Volcano disk form has been reported in Ref. [18]. Pal and coworkers studied the influence of a uniform magnetic field on the impurity-related OACs and refractive index changes in QD/QR with parabolic-inverse squared potential [19]. On the other hand, the smooth behavior of Gaussian-type potential at QD boundaries enables us to model compositional modulation within the QDs [20] and handle the excitations, ionization and tunneling processes in nanostructures [21]. Considering the practicality of Gaussian attractive confinement potential, from the aspect of numerical calculations, results of the studies conducted on QRs modeled with a Gaussian-type potential reveal tunability of the electronic and optical properties of nanostructures through the modification of the geometric parameters. [22–25]. An essential pillar of technological development is discovering materials with functional properties. One way to do this is to tune the properties of materials by controlling the irregularities/impurities within them [26–28]. One of the critical factors in determining the semiconductor-based device performance relies on the precise control of the number and position of dopant atoms. Current nanostructure fabrication techniques made it possible the control of dopants in line with the targeted purposes [29, 30]. Moreover, nowadays single-ion implantation technique allows us to implant dopant ions one by one in a specified semiconductor region [31]. Therefore, a large number of papers involving impurity-related electronic, optical and transport responses in QDs and QRs have been reported [32–38]. Singly ionized double-donor system (D2+ ) in nanostructure is especially notable as being a promising candidate for a solid-state qubit arrangement [39–44]. D2+ molecular complex consists of two fixed positive charge centers that share a conduction band electron [43]. From the theoretical point of view, the adjustability of the positions of the charge centers makes it possible to a e-mail: (corresponding author) 0123456789().: V,-vol 123 616 Page 2 of 12 Eur. Phys. J. Plus (2024) 139:616 handle different configurational cases from the same starting model [45]. D2+ molecular complex is analogous to the singly ionized H2+ in vacuum that can be obtained by irradiating H2 gas in an ultrahigh-vacuum chamber with an intense laser [43]. Studies carried out on the electronic structure and related properties of H2+ -like impurities show that under suitable physical conditions, this structure can be considered as a quasi-two-level system in which the impurity states can be used as charge qubits [46]. The processing of information encoded in the electron spin or orbital state occurs through the manipulation of the electronic charge, which is accomplished by the application of external electric fields [47]. Furthermore, intensive studies have been carried out on the electronic structures of ternary compounds that share similar structural and electronic properties as the zincblende semiconductors with commercially potential applications [48]. Scientists are attracted to the ternary chalcogenide compounds because of their promising prospects for electro-optical, nonlinear optical and optoelectronic devices [49–51]. Tunable filters and UV photodetectors have already been developed using ternary chalcogenides, such as CdAl2 Se4 and CdGa2 Se4 , as reported in references [52], whereas HgGa2 S4 [53] is in practice for mid-infrared region applications. In a recently published study, Abubakr et al. employed the full potential linearized augmented plane wave technique to investigate the optoelectronic and elastic properties of Cu-based ternary chalcogenides [54]. The authors concluded that these compounds e (...truncated)