A 3D topological insulator quantum dot for optically controlled quantum memory and quantum computing Hari P. Paudel and Michael N. Leuenberger ∗ NanoScience Technology Center and Department of Physics, University of Central Florida, Orlando, Florida 32826, United States We present the model of a quantum dot (QD) consisting of a spherical core-bulk heterostructure made of 3D topological insulator (TI) materials, such as PbTe/Pb0.31Sn0.69Te, with bound massless and helical Weyl states existing at the interface and being confined in all three dimensions. The number of bound states can be controlled by tuning the size of the QD and the magnitude of the core and bulk energy gaps, which determine the confining potential. We demonstrate that such bound Weyl states can be realized for QD sizes of few nanometers. We identify the spin locking and the Kramers pairs, both hallmarks of 3D TIs. In contrast to topologically trivial semiconductor QDs, the confined massless Weyl states in 3D TI QDs are localized at the interface of the QD and exhibit a mirror symmetry in the energy spectrum. We find strict optical selection rules satisfied by both interband and intraband transitions that depend on the polarization of electron-hole pairs and therefore give rise to the Faraday effect due to Pauli exclusion principle. We show that the semi-classical Faraday effect can be used to read out spin quantum memory. When a 3D TI QD is embedded inside a cavity, the single-photon Faraday rotation provides the possibility to implement optically mediated quantum teleportation and quantum information processing with 3D TI QDs, where the qubit is defined by either an electron-hole pair, a single electron spin, or a single hole spin in a 3D TI QD. Remarkably, the combination of inter- and intraband transition gives rise to a large dipole moment of up to 450 Debye. Therefore, the strong-coupling regime can be reached for a cavity quality factor of Q ≈ 10 4 in the infrared wavelength regime of around 10 μm. KEYWORDS: topological insulator, quantum dot, heterostructure. PACS numbers: 81.07.Ta,73.40.-c,78.66.-w,78.20.Ls I. INTRODUCTION 3D TIs are narrow-bandgap materials with topologi- cally protected gapless surface/interface states that are characterized by the linear spectrum of massless Weyl fermions. 1,2 In such materials, the spins of the Kramers pairs are locked at a right angle to their momenta on the Fermi surface due to spin-orbit coupling, 3–9 which can be used for spin current generation. 10–12 The surface states are protected by time reversal symmetry, leading to sup- pression of backscattering from edges and nonmagnetic impurities. 1,2,6,13,14 Such states are of great importance in low-power opto-spintronics. 10,15 Decoherence can be circumvented by highly polarized spin states with helical spin texture, 3,16–18 leading to a phase coherence length of several hundred nanometers in nanostructures. 19,20 In 3D TI nanostructures the special properties of topo- logically protected surface states of TIs are amplified be- cause of the large surface-to-volume ratio. In addition, the chemical potential can be electrically tuned using a gate voltage. For example, the coherent propagation of the Weyl electrons around the perimeter of a nanoribbon provides excellent evidence of the topological nature of the surface states in TI nanostructures. 20 Experiments on both the physical and chemical synthesis of TI nanos- tructures have been done recently to understand their transport properties at the nanoscale. 21–23 Recently, in a TI QD with tunable barriers based on ultrathin Bi 2 Se 3 films, Coulomb blockade with around 5 meV charging energy was observed. 24 So far, a theoretical study of electronic properties of 2D helical states occurring at the nanoscale of 3D TIs, such as in QDs, is still lacking. In this article, we present for the first time the study of bound Weyl states that are con- fined at the interface of a spherical core-bulk heterostruc- ture QD made of 3D TI materials such as Pb 1−x Sn x Te. We show that at the interface massless Weyl fermions are confined in all three dimensions. The directions of spin and momentum are tangent to the surface of the QD. Re- markably, their inherent spin-momentum locking prop- erty exists even in a QD. Because of the linear dispersion there is a mirror symmetry in the energy spectrum be- tween positive and negative energy states, in contrast to topologically trivial semiconductors. We demonstrate that this symmetry in energy spectrum is preserved for the QD spectrum. Several methods have been proposed to implement op- tically controlled quantum memory and optically me- diated quantum computing with topologically trivial QDs. Quantum memories have been recently reviewed in Ref. 25. A recent review on optically controlled quantum computing with electron spins can be found in Ref. 26. Optically controlled single-electron spin memory has been experimentally demonstrated using GaAs QDs 27 and InGaAs QDs. 28 Exciton memory has been implemented experimentally in a semiconductor nanopost. 29 For the purpose of using a hole spin as quan- tum memory or qubit, high coherence of hole spins in InGaAs QDs has been experimentally shown. 30 Ref. 31 demonstrates experimentally that a single spin can be arXiv:1212.6772v2 [cond-mat.mes-hall] 1 Jun 2013