Physics Letters A 375 (2011) 651–656 Contents lists available at ScienceDirect Physics Letters A www.elsevier.com/locate/pla Combined Aharonov–Bohm and Zeeman spin-polarization effects in a double quantum dot ring Eric R. Hedin, Abigail C. Perkins, Yong S. Joe ∗ Center for Computational Nanoscience, Department of Physics and Astronomy, Ball State University, Muncie, IN 47306-0505, USA article info abstract Article history: Received 23 September 2010 Received in revised form 1 November 2010 Accepted 11 November 2010 Available online 13 November 2010 Communicated by R. Wu Keywords: Aharonov–Bohm ring Quantum dots Zeeman splitting Spin-polarization A mesoscale Aharonov–Bohm (AB) ring with a quantum dot (QD) embedded in each arm is computation- ally modeled for unique transmission properties arising from a combination of AB effects and Zeeman splitting of the QD energy levels. A tight-binding Hamiltonian is solved, providing analytical expressions for the transmission as a function of system parameters. Transmission resonances with spin-polarized output are presented for cases involving either a perpendicular field, or a parallel field, or both. The combination of the AB-effect with Zeeman splitting allows sensitive control of the output resonances of the device, manifesting in spin-polarized states which separate and cross as a function of applied field. In the case with perpendicular flux, the AB-oscillations exhibit atypical non-periodicity, and Fano-type resonances appear as a function of magnetic flux due to the flux-dependent shift in the QD energy levels via the Zeeman effect.  2010 Elsevier B.V. All rights reserved. 1. Introduction Classical electronics exploits the electron charge to designate binary information, whereas spintronics is an emerging field in which the spin of the electron is used for switching purposes and to communicate information [1]. Spin-dependent effects arise from interactions of the electron with an external magnetic field or with magnetic properties of the conduction material. An important fea- ture of an AB interferometer with a quantum dot (QD) embedded in one or both arms is the ability to probe the total spin of the electronic state of the QD. The investigation of electron-spin trans- port in semiconductor nanostructures and nanoscale electronic devices has attracted recent attention [2–4]. Quantum dots offer unique possibilities for manipulating and utilizing the spin of elec- trons in individual quantum states. The main topics of research have focused on studying the fundamental aspects of the spin- dependent transport (e.g. spin coherence times, many-body effects such as the Kondo effect or spin–charge separation [5,6], and spin- dependent tunneling [7]) and to developing and optimizing semi- conductor spintronics device applications, such as spin transistors and spin qubits [2]. Experimental work [8] has shown interesting flux-dependence of the total wave function, including the spin and orbital elec- tron configuration of the two coupled QDs. Experiments have also shown the possibility of the existence of long-lived spin states in quantum dots [2]. The spin relaxation rate in quantum dots is ex- * Corresponding author. E-mail address: ysjoe@bsu.edu (Y.S. Joe). pected to be very low because of forbidden transitions. By this we mean that the spin of the electron can only couple to the envi- ronment indirectly through the spin–orbit coupling, which renders the spin fairly stable against random charge fluctuations [9]. The electron spin is assumed to be conserved as it tunnels in and out of the QD. Coherence, spin-decoherence, and resonant phenom- ena are very important for quantum computing applications. In addition, experimental demonstration of spin filtering controlled by gate voltages in a semiconductor QD has been observed [10]. Hanson et al. demonstrated clear Zeeman splitting of the two- electron triplet states of GaAs QDs by applying a large magnetic field ( B ‖ = 12 T) parallel to the plane of the 2DEG [11]. Spin–orbit interactions are negligible in their results, which minimizes mixing of the spin states, even with a large parallel field [12]. Elsewhere, it has been proposed that Fano resonances [13] associated with electron transmission through open QDs can give rise to spin po- larization [14]. Our recently investigated results on sharpened AB oscillations for parallel double QDs in resonance [15] suggest an- other feasible mechanism for spin polarization or filtering of spin states with energy splitting. When the transmission resonance is a sharp function of energy or magnetic field, opposite electron spin states should be transmitted with a high degree of polarization. In this article, an AB-ring with a QD embedded in each arm is analyzed for the scenario in which a perpendicular external mag- netic field contributes not only an AB phase shift but also Zeeman splitting of the electron energy states in the two QDs. We in- vestigate spin-quantum states by studying interference effects in the transmission resulting from the application of external mag- netic fields to this device. In the current work, resonant transport through QDs embedded in the arms of an AB-ring is studied by 0375-9601/$ – see front matter  2010 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2010.11.030