Abstract. -The effect of Rashba spin-orbit (SO) interaction on the hole states in a quantum dot is studied in the presence of an external magnetic field. We demonstrate here that the Rashba SO coupling has a profound effect on the energy spectrum of the holes revealing level repulsions between the states with the same total momentum. We also show that the resulting spin-orbit gap is much larger than the corresponding one for the electron energy levels in a quantum dot. Inter-hole interactions only marginally reduce the spin-orbit gap. This enhanced Rashba effect would manifest itself in the tuneling current which depends on the spin-orbit coupling strength.Introduction. -Semiconductor quantum dots are the nanoscale zero-dimensional systems with discrete energy levels, much like in atoms (and hence the popular name, artificial atoms [1]). They have one great advantage that their shape and the number of electrons in those systems can be controlled externally and as a result, they have been the subject of intense research in recent years. They are particularly promising as components of futuristic devices for quantum information processing [2] and for coherent spin transport [3]. The spin states of these systems are ideal for applications because of their relative insensitivity to electrical noise in a device environment [4]. One proposed mechanism for coherent spin manipulation in quantum nanostructures is via the Rashba spin-orbit (SO) coupling [5,6]. The SO interaction can arise in a quantum dot due to confinement and lack of inversion symmetry of the nanostructure which creates a local electric field perpendicular to the electron plane [7,8]. The SO coupling strength can be varied by changing the asymmetry of the quantum structure with an external electric field. The magnetic field effects on the properties of lowdimensional systems, such as quantum wells and quantum dots with the Rashba interaction has been reported in experiments [9] and theory [10]. In our work on Rashba effects in electron dots [11], we found multiple level crossings and level repulsions that resulted from the interplay between the Zeeman and the SO couplings. Level anticrossings observed in quantum nanostructures have been attributed to the presence of SO coupling in those systems [12]. However, studies of the Rashba effect on quan-

The electronic states and optical transitions of a ZnO quantum ring containing few interacting electrons in an applied magnetic field are found to be very different from those in a conventional semiconductor system, such as a GaAs ring. The strong Zeeman and Coulomb interaction of the ZnO system, exert a profound influence on the electron states and on the optical properties of the ring. In particular, our results indicate that the Aharonov-Bohm (AB) effect in a ZnO quantum ring strongly depends on the electron number. In fact, for two electrons in the ZnO ring, the AB oscillations become aperiodic, while for three electrons (interacting) the AB oscillations completely disappear. Therefore, unlike in conventional quantum ring topology, here the AB effect (and the resulting persistent current) can be controlled by varying the electron number.In a quantum ring structure of nanoscale dimension, the confined electrons exhibit a topological quantum coherence, the celebrated Aharonov-Bohm (AB) effect [1]. The characteristics of the energy spectrum (noninteracting) for a ring-shaped geometry, pierced by a magnetic flux Φ, correspond to a periodically shifted parabola with period of one flux quantum, Φ 0 = h/e [2]. All physical properties of this system, most notably, the persistent current (magnetization) [3] and optical transitions [4], have this periodicity. Experimental observations of the AB effect were reported in metal rings [5] and in semiconductor rings [6]. Persistent currents were also measured in metal [7] and semiconductor [8] rings. The role of electron-electron interactions on the AB effect was explored systematically via the exact diagonalization scheme for few interacting electrons in a quantum ring [9,10]. Interactions were found to introduce fractional periodicity of the AB oscillations [11]. Major advances in fabrication of semiconductor nanostructures have resulted in creation of nanoscale quantum rings in e.g., GaAs and InAs systems containing only a few electrons [12,13]. In those experiments, the AB effect manifests itself in optical transitions [11,14], and magnetoconductance [15]. The electron energy spectrum in a ring geometry has also been measured [16]. Those experiments have confirmed the theoretical predictions about the influence of electron-electron interactions on the persistent current, that was previously predicted [10,12,13]. The AB effect has also been studied in Dirac materials, such as graphene [17], both theoretically [18] and experimentally [19]. One major advantage of all these nanoscale quantum rings is that here the ring size and the number of electrons in it can be externally controlled [12,13].In all these years, for investigations of nanoscale quantum structures, such as the quantum dots (QDs) (or, the artificial atoms) [20,21] and quantum rings (QRs), * Tapash.Chakraborty@umanitoba.ca the materials of choice had been primarily the conventional semiconductors, viz. the GaAs or InAs heterojunctions, where the high-mobility two-dimensional electron gas (2DEG) was quantum con...

Intense terahertz laser field is shown to have a profound effect on the electronic and optical properties of quantum rings, where the isotropic and anisotropic quantum rings can now be treated on equal footing. We have demonstrated that in isotropic quantum rings the laser field creates irregular AB oscillations that are usually expected in anisotropic rings. Further, we have shown for the first time that intense laser fields can restore the isotropic physical properties in anisotropic quantum rings. In principle, all types of anisotropies (structural, effective masses, defects, etc.) can evolve as in isotropic rings, in our present approach. Most importantly, we have found a continuous evolution of the energy spectra and intraband optical characteristics of structurally anisotropic quantum rings to those of isotropic rings, in a controlled manner, with the help of a laser field.Research on the electronic and optical properties of quantum confined nanoscale structures, such as quantum dots and quantum rings has made great strides in recent years in unraveling new phenomena and their enormous potentials in device applications. In this context, quantum rings with its doubly-connected structure attracts special attention. Its unique topolocal structure provides a rich variety of fascinating physical phenomena in this system. Observation of the Aharonov-Bohm (AB) oscillations [1] and the persistent current [2] in small semiconductor quantum rings (QR), and recent experimental realization of QRs with only a few electrons [3,4] have made QRs an attractive topic of experimental and theoretical studies for various quantum effects in these quasione-dimensional systems [5]. In particular, recent work has indicated the great potentials of QRs as basis elements for a broad spectrum of applications, starting with terahertz detectors [6], efficient solar cells [7] and memory devices [8], through electrically tunable optical valves and single photon emitters [9,10]. We have also worked previously on QRs in new materials such as graphene systems [11] and ZnO [12] with interesting outcomes reported in [13] and [14] respectively.Although almost circular or slightly oval shaped QRs have been fabricated by various experimental groups [15][16][17][18], anisotropic QRs are the ones most commonly obtained during the growth process [17,[19][20][21]. Theoretically the effect of anisotropy on electronic, magnetic and optical properties of quantum rings have been investigated by various authors [22][23][24][25][26]. In those studies, different types of anistropies were explored. For example, in Ref. [22,24,25] the shape anisotropy of the QR was considered, while in Ref.[23] the anisotropy associated with defects was studied, and in [26] the effective mass anisotropy was investigated. In all these cases it was shown that the anisotropy can dramatically alter the AB oscillations in the QR. In particular, in Ref. [26] it was demonstrated that the unusual AB oscillations caused by the effective mass anisotropy in the QR can be converted to u...

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