PHYSICAL REVIEW B 95, 205409 (2017) Interplay between structure asymmetry, defect-induced localization, and spin-orbit interaction in Mn-doped quantum dots L. Cabral, 1 Fernando P. Sabino, 2 Vivaldo Lopes-Oliveira, 2 Juarez L. F. Da Silva, 3 Matheus P. Lima, 1 Gilmar E. Marques, 1 and Victor Lopez-Richard 1 1 Departamento de Física, Universidade Federal de São Carlos, 13565-905 São Carlos, São Paulo, Brazil 2 Instituto de Física de São Carlos, Universidade de São Paulo, 13560-970 São Carlos, São Paulo, Brazil 3 Instituto de Química de São Carlos, Universidade de São Paulo, 13560-970 São Carlos, São Paulo, Brazil (Received 9 December 2016; revised manuscript received 28 March 2017; published 8 May 2017) Combining atomistic methods and effective mass approaches, the magnetic field response of Mn-doped deformed quantum dots has been characterized. The defect-induced asymmetry triggers unavoidable spin-orbit coupling effects that become more relevant the smaller the quantum confinement. Thus, the expected spin splitting modulation by the exchange interaction between the confined carriers and the Mn impurity is tuned by the intertwining of spatial geometry and magnetic field. Furthermore, ab initio calculations are presented for assessing the exchange interaction term and its response to confinement effects at the atomistic level. DOI: 10.1103/PhysRevB.95.205409 I. INTRODUCTION Although disorder and defects are considered to be detri- mental to the thorough control of the expected functionalities of nanoscopic systems, they can be unavoidable, at least up the limits determined by the current synthesis technologies [1]. Quite recently, considerable attention has been paid to defect control in quantum dot (QD) architectures for tuning their optical blinking [2], charge transport [3], or even implementing building blocks for spin memories [4]. In the case of QDs, in particular for those with small size, their surfaces play a role in the appearance of lattice defects and impurity diffusion [5]. These, in turn, become critical elements in the process of intentional doping either with diluted or with solitary dopants [6]. Assessing and predicting the relative effect of disorder poses reasonable difficulties, in particular, using ab initio atomistic simulations due to the large size of real life QDs. Thus, theoretical models based on Hamiltonian models such as the k·p can be used [7,8]; however, from our knowledge, most of those models usually assume symmetric QD structures. This is even more complex when taking into account externally applied electromagnetic fields. Additionally challenging is the modeling of semiconductor QDs doped with magnetic impuri- ties that demands the emulation of the interplay of confinement asymmetries, exchange interaction, and spin-orbit coupling [9,10]. It is important to notice that an atomistic analysis of the elements creating a disorder, such as impurity localization, structural defects, and perturbations generated by localized magnetic moments, elucidates the origin and the profile of the asymmetries, and hence those effects can be included in Hamiltonian models such as the k·p model; however, there are several challenges that remain to be overcome, e.g., an analytical solution that helps to identify the key factors that define the physical properties. To contribute to the solution of those problems, which is a challenge for several theoretical approaches, in particular the addition of external fields, the present paper has the aim to obtain a comprehensive description of the way that defects in QDs scale with confinement, deformation strength, and position for the center of QD by the combination of ab initio density functional theory calculations within the k·p Hamiltonian model. This approach will help elucidating and contrasting how each of these contributions affect the magnetic response. In particular, we shall characterize the asymmetry tuning of the effective Zeeman splitting and the ground-state character in the conduction band. Exact analytical expressions are derived in the low-field limit that allow the correlation of all the effects in a systematic way including the impurity positioning. Hence, we shall provide a qualitative contrast with the expected result for perfectly symmetric systems as those reported in Refs. [11,12]. Con- trasting different symmetry configurations allows building a realistic picture of the plausible ways the Mn is incorporated in the system. The effective mass model of the electronic structure allows emulating confinement profiles with control- lable symmetry lowering, spin-orbit interaction effects, and external fields under a variety of configurations in a systematic way. The effective mass model will be complemented with ab initio atomistic simulations based on density functional theory employing a small model system to represent the QD systems embedded in a semiconductor frame. Furthermore, the connection between the effective mass model and ab initio calculations was done through the study of the most important trends such as the location of the substitutional Mn within the QD frame, as well as an estimation for the exchange interaction term. This combination allowed us to assess the role played by strain and confinement environment on the electronic properties of the system with different degrees of Mn incorporation. II. MODELING OF QUANTUM DOTS USING k · p METHOD We characterized the impurity incorporation effects in QDs using an effective mass model with a tunable confinement potential profile. In our calculations, the modulation of the Lande factor allows assessing the role of the asymmetries and the spin-orbit coupling. 2469-9950/2017/95(20)/205409(6) 205409-1 ©2017 American Physical Society