Session P14: Focus Session: Spins in Semiconductors - Quantum Dots and Qubits

Magnetic Polarons and Bipolarons in Quantum Dots

Magnetically doped (typically by Mn) semiconductor quantum dots (QDs) allow a control of magnetic ordering in ways not available in the bulk. For example, onset of magnetism can be realized by adding a single carrier or changing symmetry of the quantum confinement, even at a fixed carrier number [1]. Recent experiments revisit the concept of magnetic polaron [2], formed when a single carrier added to a QD aligns the Mn spins through exchange interaction. The experiments [3,4] show that the induced magnetization persists at relatively high temperatures. First, we discuss a QD system, in which the experimental magnetic polaron energy, in addition to its relatively high value, shows a surprisingly weak temperature dependence [4]. We explain this effect by magnetic anisotropy of the QD. Next, we turn to the case where a magnetic QD contains two carriers. We find theoretically that Mn spins align, forming a magnetic 'bipolaron', even when the ground state has zero carrier-spin [5]. The corresponding state breaks spatial symmetry, unlike in the case of a single magnetic polaron. We propose experimental tests of our prediction. We also explore the stability of the broken-symmetry state with zero net magnetization versus other patterns of magnetization [6]. Finally, we show some interesting consequences of diffusive coupling of a magnetic QD to a reservoir of carriers [7]. This work was done in collaboration with P. Stano, J. Pientka, A. Petukhov, and I. Zutic.\\[4pt] [1] R. M. Abolfath, et al. Phys. Rev. Lett. 101, 207202 (2008).\\[0pt] [2] Maksimov, A. et al. Phys. Rev. B 62, R7767 (2000), J. Seufert et al., Phys. Rev. Lett. 88, 027402 (2002).\\[0pt] [3] R. Beaulac et al., Science 325, 973 (2009).\\[0pt] [4] I. R. Sellers, et al., Phys. Rev. B 82, 195320 (2010).\\[0pt] [5] R. Oszwaldowski, et al., Phys. Rev. Lett. 106, 177201 (2011)\\[0pt] [6] P. Stano, R. Oszwaldowski, A. G. Petukhov, and I. Zutic, preprint.\\[0pt] [7] J. M. Pientka, R. Oszwaldowski, A. G. Petukhov, J. E. Han and I. Zutic, Reentrant Magnetic Polaron Formation in Quantum Dots, preprint.   

Reentrant Magnetic Polaron Formation in Quantum Dots

Recently, there have been several theoretical studies that show multiple ways of manipulating magnetic ordering in Quantum Dots (QD) [1,2]. Experiments [3,4] display the formation of Magnetic Polarons in both colloidal and self-assembled QDs. We focus on a type-II QD band profile, where the electrons reside in the barrier, while the holes are localized in the QD interior, which contains the magnetic impurities. In our model, photo-excitation of carriers induces a quasi equilibrium. We consider various QD states to describe the carrier-mediated magnetic ordering in QDs. Allowing for different QD states changes the magnetic properties due to different carrier spin density [5], which affects the alignment of the magnetic impurities. [1] R. M. Abolfath, A. G. Petukhov, and I. Zutic, Phys. Rev. Lett. 101, 207202 (2008); [2] I. Zutic and A. G. Petukhov, Nature Mater.4, 623 (2009). [3] R. Beaulac et al., Science 325, 973 (2009). [4] I. R. Sellers, R. Oszwaldowski, et al., Phys. Rev. B 82, 195320 (2010). [5] J. M. Pientka, R. Oszwaldowski, A. G. Petukhov, J. E. Han, and I. Zutic, Reentrant Magnetic Polaron Formation in Quantum Dots, preprint.   

Magnetic anisotropies of quantum dots

Magnetic anisotropies in quantum dots (QDs) doped by magnetic ions are discussed in terms of two frameworks: anisotropic g-factors and magnetocrystalline anisotropy energy [1]. Two examples, related to zinc-blende $p$-doped materials, are given of how these frameworks are utilized: four-level Hamiltonian of a flat QD and a cuboid infinite-well QD containing a single hole. The latter model, despite being an idealization of a real QD, displays a rich phenomenology of anisotropies. We quantify the anisotropy constants for ZnSe and CdTe QDs, confirming that the Ising-like effective Hamiltonians apply to magnetic QDs [2]. Compared to bulk systems, confinement tuning offers a new way to control easy axes in magnetic QDs. [1] K. Vyborny et al., preprint (2011). [2] C. Le Gall et al., Phys. Rev. Lett. 107, 057401 (2011).   

The Interplay of Electronic Properties and Magnetic Anisotropy in Quantum Dots

Tunability of magnetic anisotropy (MA) in nanostructures is a fascinating topic, for both fundamental understanding of nanomagnetism and possible spintronic applications. While there have been preceding efforts to systematically study the MA in bulk [1], we still lack a fundamental understanding of that in magnetic quantum dots (QDs). We first explore electronic properties of nonmagnetic QDs that can be significantly altered from the bulk-state depending upon the material and geometry. Focusing on II-VI materials forming both cubic and non-cubic QDs, we confirm qualitatively different energy spectra between different materials [2]. These findings can guide the control of MA in magnetic QDs. Supported by DOE-BES, NSF-DMR, AFOSR-DCT, U.S. ONR, and NSF-ECCS. \\[4pt] [1] X. Liu, Y. Sasaki and J. K. Furdyna, Phys. Rev. B 67, 205204 (2004). \\[0pt] [2] K. V\'yborn\'y, J.E. Han, R. Oszwadowski, I. \v{Z}uti\'c, and A. G. Petukhov, preprint (2011).   

Theory of collective quantum effects of the nuclear spin bath in a Ge/Si core/shell nanowire quantum dot

We study a quantum-dot spin-valve setup with a uniform hyperfine coupling of the electron spin to the nuclear bath. We propose Ge/Si core/shell nanowire quantum dots as a promising platform in which, through engineering of the nuclear spin positions and of the radial and longitudinal electron confinement, a nearly uniform hyperfine interaction can be realized. The dynamics of this coupled system are exactly soluble in terms of collective nuclear states with fixed total angular momentum. We theoretically show that the quantum-mechanical properties of such collective states of the nuclear spins can be probed through electron transport in this spin-valve setup. The associated transport current shows an enhancement due to coupling to collective modes in the nuclear-spin system directly analogous to the problem of superradiance in quantum optics. This effect is robust to dephasing of the nuclear spins and would provide a demonstration of large-scale collective quantum effects in a nuclear-spin system.   

Magnetotransport in Ge/Si Quantum Dot Molecules Fabricated by Directed Self-Assembly

The electronic states of strained self-assembled Ge quantum dots embedded in silicon provide an attractive system for controlling electron spin interactions via direct exchange\footnote{C. E. Pryor, M. E. Flatte, and J. Levy, Applied Physics Letter \textbf{95}, 232103 (2009)} . Directed self-assembly of sub-10 nm Ge islands are fabricated to produce laterally coupled quantum dot molecules with geometrically-defined spin exchange couplings. Ge islands are coupled to the Si capping layer, and geometries can be defined that are suitable for either vertical or lateral transport. We describe low-temperature vertical magneto-transport measurements on individual and small arrays of Ge islands grown on SOI substrate. Characteristic features in the magnetotransport are observed that correspond to specific geometrical arrangements of the quantum dots.   

Singlet-triplet splitting in double dots due to spin orbit and hyperfine interactions

We analyze the low-energy spectrum of a detuned double quantum dot in the presence of magnetic fields, spin orbit interaction, and nuclear spins, and focus on the regime of spin blockade. Starting from a realistic model for two interacting electrons in a double dot, we derive perturbatively an effective two-level Hamiltonian in the vicinity of an avoided crossing between singlet and triplet levels, which are coupled by the spin-orbit and hyperfine interactions. We evaluate the level splitting at the anticrossing in various parameter regimes, and show that it depends on two controllable parameters: the angle between the external magnetic field and the internal spin orbit field, and on the detuning, as well as on the difference between nuclear fields in the two dots. We identify a parameter regime where spin orbit and hyperfine terms can become of equal strength and propose a protocol for tuning their relative sizes.   

Single-shot correlations and two-qubit gate of solid-state spins

Recent advances in nanotechnology and quantum engineering have made it possible to probe single spins in the solid-state. Here we report independent single-shot read-out of two electron spins in a double quantum dot. The read-out method is all-electrical, cross-talk between the two measurements is negligible, and read-out fidelities are $\sim$ 86\% on average. This allows us to directly probe the anti-correlations between two spins prepared in a singlet state and to demonstrate the operation of the two-qubit exchange gate on a complete set of basis states. Ongoing work focuses on integration with single-spin rotations, scaling and extending coherence times.\\[4pt] K.C. Nowack, M. Shafiei, M. Laforest, G.E.D.K. Prawiroatmodjo, L.R. Schreiber, C. Reichl, W. Wegscheider and L. M. K. Vandersypen, Single-shot correlations and two-qubit gate of solid-state spins, Science 330, 1269 (2011)   

Spin-orbit effects on the full dynamics of double quantum dot qubit states

We study spin-obit interaction (SOI) and relaxation effects on the measurement of the extended singlet state return probability $P(S)$ in a double quantum dot (DQD) system with two electrons, in the presence of hyperfine interaction (HFI) and weak external magnetic fields. Using appropriate pulse cycles to change the detuning between the two quantum dots, we describe the full dynamical behavior of the system taking into account the complete set of states. We find that the mixing of the $m_s =1\;(T_+ )$ triplet with the (0,2) local singlet, induced by SOI via non-spin-conserving tunneling transitions, has an important effect on the measurement of $P(S)$, and a clear experimental signature. The numerical results are also analyzed in terms of a Feshbach projection to the effective low-energy dynamics, which explain the role of SOI on the relaxation and overall dynamics relevant in experiments. We also explore the case of the Landau-Zener-St\"{u}ckelberg interferometry realized via voltage sweeps through the $S-T_+ $anticrossing generated by HFI in the DQD energy spectrum [1]. We focus on studying the effects of SOI and relaxation on the interferometric properties of the system in this regime. [1] J.R. Petta, H. Lu and A.C. Gossard, Science 327, 669 (2010).   

Spin blockade in a triple silicon quantum dot in CMOS technology

We study the spin blockade (SB) phenomenon by quantum transport in a triple quantum dot made of two single electron transistors (SET) on a CMOS platform separated by an implanted multiple donor quantum dot [1]. Spin blockade condition [2] has been used in the past to realize single spin localization and manipulation in GaAs quantum dots [3]. Here, we reproduce the same physics in a CMOS preindustrial silicon quantum device. Single electron quantum dots are connected via an implanted quantum dot and exhibit SB in one current direction. We break the spin blockade by applying a magnetic field of few tesla. Our experimental results are explained by a theoretical microscopic scheme supported by simulations in which only some of the possible processes through the triple quantum dot are spin blocked, according to the asymmetry of the coupling capacitances with the control gates and the central dot. Depending on the spin state, the SB may be both lifted and induced. Spin control in CMOS quantum dots is a necessary condition to realize large fabrication of spin qubits in some solid state silicon quantum device architectures.\\[0pt] [1] Pierre et al., Appl. Phys. Lett., 95, 24, 242107 (2009); [2] Liu et al., Phys. Rev. B 77, 073310 (2008); [3] Koppens et al., Nature 442, 766-771 (2006)   

Spin-orbit effects in triple dot quantum shuttles

Within the framework of a fully quantum mechanical approach we use a generalized density matrix formalism to study the spin-orbit coupling effects in a triple dot quantum shuttle. An interesting feature of this type of nanoelectromechanical systems is that the interplay between the electronic, spin, and mechanical degrees of freedom give rise to novel transport phenomena that has attracted a great deal of interest in both the applied and basic research. In this work, the effect of spin-orbit coupling is incorporated into the system by introducing non spin-conserving tunneling elements between the quantum dots. We explore the features of spin-polarized current by changing the Zeeman-split levels of the dots, and the frequency of the oscillating central dot. We show that the spin-orbit effect manifests itself as sidebands in the spin-polarized current, and that the tunneling channels can be controlled by adequately tuning the relative energies of the Zeeman-split levels, and by manipulating the current contribution from the vibrational modes.