Session Y42: Solid-State Hole Spin Qubits

Hole spins as qubits in gated lateral devices – opportunities and challenges

In semiconductor materials, the wave functions of holes are built from p-type atomistic orbitals. This leads to a weaker hyperfine interactions of the hole spin with nuclear lattice spins and thus promises longer coherence times compared to those of electron spins [1,2]. However, holes are also subject to much stronger spin-orbit (SO) interactions. This talk explores the new physics brought about by the SO interaction for few carrier systems and discusses how it influences the magneto-transport spectra of GaAs lateral double quantum dots (DQD) populated by one or two holes [3,4]. In contrast with DQDs fabricated in Si, where the SO interaction is much weaker [5], in GaAs two-hole DQD the Pauli spin blockade is found to be absent except for the regime of very small magnetic fields. A simple theoretical model, accounting for both the usual spin-conserving and the spin-flipping tunneling (SFT) processes, is introduced. The magnitudes of both elements, extracted from single-hole photon-assisted tunneling, are shown to be similar and strongly dependent on the magnetic field. While the SFT process complicates the usual spin-to-charge conversion process, it enables fast hole spin rotations by electrostatic means. [1] J. Fisher, W. A. Coish, D. V. Bulaev, and D. Loss, Phys. Rev. B 78, 155329 (2008). [2] B. D. Gerardot et al., Nature 451, 441 (2008). [3] L. A. Tracy, T. W. Hargett, and J. L. Reno, Appl. Phys. Lett. 104, 123101 (2014). [4] A. Bogan, S. Studenikin, M. Korkusinski G. Aers, L. Gaudreau, P. Zawadzki, A. Sachrajda, L. Tracy, J. Reno, and T. Hargett, Phys. Rev. Lett. (submitted). [5] R. Li, F. E. Hudson, A. S. Dzurak, and A. R. Hamilton, Nano Lett. 15, 7314 (2015). Collaborating Authors: A. Bogan, S. Studenikin, G. Aers, L. Gaudreau, P. Zawadzki, A. Sachrajda (NRC, Canada), L. Tracy, J. Reno, and T. Hargett (Sandia National Laboratories, USA)   

A CMOS silicon hole spin qubit

Hole spins in silicon represent a promising direction for solid-state quantum computation, possibly combining fast qubits [1] with limited hyperfine interaction. We report on a qubit device implemented on a foundry-compatible Si CMOS platform [2]. The device, fabricated using SOI NanoWire MOSFET technology, is in essence a two-gate pFET. The qubit is encoded in the spin degree of freedom of a hole quantum dot defined by one of the gates, while the second gate defines another quantum dot used for the qubit initialization and readout. All electrical, two-axis control of the spin qubit is achieved by applying a phase-tunable microwave modulation to one of the gate. We demonstrate fast coherent oscillations with Rabi frequencies as high as 80MHz with an inhomogeneous dephasing time of T$_{2}^{\ast \, }$\textasciitilde 60ns [3]. By demonstrating a hole spin qubit functionality in a conventional transistor-like layout and process flow, this result bears relevance for the future up-scaling of qubit architectures. [1]- Voisin, B. \textit{et al.} \textit{Nano Lett.} \textbf{16,} 88--92 (2016). [2]- Hutin, L. \textit{et al.} \textit{IEEE Symp. VLSI Technol.} 1--2 (2016). [3]- Maurand, R. \textit{et al.} \textit{Arxiv Prepr. arXiv1605.07599v1} (2016).   

Fast Single-Shot Hold Spin Readout in Double Quantum Dots

Solid state spin qubits in quantum dots hold promise as scalable, high-density qubits in quantum information processing architectures. While much of the experimental investigation of these devices and their physics has focused on confined electron spins, hole spins in III-V semiconductors are attractive alternatives to electrons due to the reduced hyperfine coupling between the spin and the incoherent nuclear environment. In this talk, we will discuss a measurement protocol of the hole spin relaxation time $T_1$ in a gated lateral GaAs double quantum dot tuned to the one and two-hole regimes, as well as a new technique for single-shot projective measurement of a single spin in tens of nanoseconds or less. The technique makes use of fast non-spin-conserving inter-dot transitions permitted by strong spin-orbit interactions for holes, as well as the latching of the charge state of the second quantum dot for enhanced sensitivity [1]. This technique allows a direct measurement of the single spin relaxation time on time-scales set by physical device rather than by limitations of the measurement circuit. [1] S. A. Studenikin, J. Thorgrimson, G. C. Aers, A. Kam, P. Zawadzki, Z. R. Wasilewski, A. Bogan and A. S. Sachrajda, Appl. Phys. Lett. 101, 233101 (2012)   

Anisotropic Pauli Spin Blockade of Holes in a GaAs Double Quantum Dot

Electrically defined semiconductor quantum dots are appealing systems for spin manipulation and quantum information processing. Thanks to the weak hyperfine interaction and the strong spin-orbit interaction, heavy-holes in GaAs are promising candidates for all-electrical spin manipulation. However, making stable quantum dots in GaAs has only become possible recently, mainly because of difficulties in device fabrication and device stability. Here we present electrical transport measurements of heavy-holes in a lateral double quantum dot based on a $\mathrm{GaAs/Al_xGa_{1-x}As}$ heterostructure. We observe clear Pauli spin blockade and show that the lifting of the spin blockade by an external magnetic field is extremely anisotropic. Numerical calculations of heavy-hole transport through a double quantum dot in the presence of strong spin-orbit interaction demonstrate quantitative agreement with experimental results, which indicates that the observed anisotropy can be explained by the anisotropic hole g-factor and the surface Dresselhaus spin-orbit coupling.   

Suppression of Pauli Spin Blockade in Few Hole Laterally Gated Double Quantum Dots.

Hole spins have attracted increasing attention as candidates for qubits in quantum information applications. The p-type character of their wavefunction leads to smaller hyperfine interaction with the nuclei resulting in longer coherence times. Additionally, strong spin-orbit interaction allows for enhanced all-electrical manipulation of spin qubit states. Single hole spins have been electrically studied in InSb [1] and Si [2] nanowire quantum dots, however, electrostatically confined hole spins in a 2D hole gas have thus far been limited to the many hole regime. In this talk we will present a full description of the two-hole spin spectrum in a lateral GaAs/AlGaAs double quantum. High-bias magneto-transport spectroscopy reveals all four states of the spectrum (singlet and triplets) in both the (1,1) and (2,0) configurations, essential for spin readout based on Pauli spin blockade. We show that spin-flip tunneling between dots is as strong as spin conserving tunneling, a consequence of the strong spin-orbit interaction. This suppresses the Pauli spin blockade. Our results suggest that alternate techniques for single hole spin qubit readout need to be explored. [1] Pribiag et al. Nat. Nanotech. 8, 170 (2013) [2] Voisin et al. Nano Lett. 16, 88 (2016)   

Accurate hyperfine tensors for electrons and holes in Si and GaAs

Knowing (and controlling) hyperfine interactions in semiconductor nanostructures is important for quantum information processing with electron, hole, and nuclear-spin states. Through a combination of first-principles density-functional theory calculations and $\mathbf{k}\cdot\mathbf{p}$ corrections, we have found accurate hyperfine tensors for electrons and holes in GaAs and Si. Our results indicate significant corrections to previous theoretical estimates for the hyperfine coupling of electrons in GaAs and Si, but are consistent with earlier experimental measurements on Knight shifts and Korringa relaxation. In addition, we make new predictions for the hyperfine tensors of both heavy and light holes in the valence band. These calculations are consistent with $T_2^{\ast}$ times very recently measured for heavy holes in Si quantum dots [1], and with recent measurements on hole spins in InGaAs quantum dots showing an Ising-like hyperfine coupling [2]. [1] Maurand et al., arXiv:1605.07599 (2016). [2] Prechtel et al., Nat. Mat. 15, 981 (2016).   

Spin-orbit dynamics of single acceptor atoms in a silicon transistor

Acceptor atoms in silicon are promising candidates for spin-orbit qubits, having the possibility for all-electrical control and long-distance qubit coupling via microwave cavities. The unique properties of the acceptor based qubits arise from the spin-orbit coupling between the heavy and light hole states. We have investigated the fundamental interactions between the acceptor spin-3/2 states, on which these potential spin-orbit qubits are based. We experimentally study the spin-orbit dynamics of two interacting boron atoms located in a state-of-the-art CMOS transistor. A strong influence of the spin-orbit coupling on the acceptor states is observed by using a combination of radio frequency gate reflectometry and magneto-transport spectroscopy. Spin-selective tunneling is used as a spin-readout mechanism and used to probe the relaxation processes within this acceptor system. A hotspot behavior in relaxation rate is detected and explained by heavy-light hole mixing, allowing us to extract the coupling between heavy and light holes, an essential parameter for acceptor qubits. Furthermore, the observed two-hole excited state spectrum shows that the quantization axes of the hole spins are rotated with magnetic field. These are the first principles to control single acceptor atoms.   

Electric manipulation of a heavy hole acceptor qubit in SiGe quantum wells.

Recently, proposals of hole-based qubits in silicon have drawn considerable attention due to the strong spin-orbit interaction in the valence band. A hole bound to an acceptor in silicon reduces the cubic symmetry, allowing mixing of heavy hole and light hole states when an electric field is applied. Moreover, the presence of an interface close to the acceptor gives rise to a Rashba type spin-orbit interaction which together with the symmetry of the acceptor can be used to manipulate both heavy-hole and light-hole qubits through electric means only. In this work we study the effects of confining an acceptor into a SiGe quantum well. Due to strain within the quantum well, the qubit subspace has a predominantly heavy-hole nature. Again, both the Rashba spin-orbit interaction and the tetrahedral symmetry of the acceptor permit the manipulation of the qubit subspace through electric means, but now it is possible to take advantage of the g-factor difference between the well and the barriers to allow manipulation through the g-tensor modulation resonance technique. The presence of sweet spots and the Rabi frequency dependence on different parameters of the quantum well is discussed.   

Shell Filling and Magnetic Anisotropy In A Few Hole Silicon Metal-Oxide-Semiconductor Quantum Dot

There is growing interest in hole spin states in group IV materials for quantum information applications. The near-absence of nuclear spins in group IV crystals promises long spin coherence times, while the strong spin-orbit interaction of the hole states provides fast electrical spin manipulation methods. However, the level-mixing and magnetic field dependence of the p-orbital hole states is non-trivial in nanostructures, and is not as well understood as for electron systems. In this work, we study the hole states in a gate-defined silicon metal-oxide-semiconductor quantum dot. Using an adjacent charge sensor, we monitor quantum dot orbital level spacing down to the very last hole, and find the standard two-dimensional (2D) circular dot shell filling structure. We can change the shell filling sequence by applying an out-of-plane magnetic field. However, when the field is applied in-plane, the shell filling is not changed. This magnetic field anisotropy suggests that the confined hole states are Ising-like.   

Controlling hole spin in quantum dots

Hole spins in semiconductor quantum dots (QD) are promising qubits. The Zeeman-split states form two-level systems with splitting determined by the physical spin of the state. We show that application of a magnetic field B in Voigt configuration, in the plane of the QD, combined with a lateral electric field parallel or antiparallel to B provides exquisite control of the hole's physical spin and Zeeman splitting. We use tight-binding theory to study strained InAs/GaAs and strain-free GaAs/AlAs QDs. As a result of strong spin-orbit coupling, the hole spin is strongly polarized and locked to the QD axis for B away from the Voigt configuration. The spin polarization is nearly complete for thin QDs but is reduced for taller dots. In Voigt configuration, the hole spin is nearly fully depolarized. When an electric field is applied to push the hole to one side of the QD, strong spin polarization is recovered. The z-component of the spin can be parallel or antiparallel to the QD axis, depending on the direction of B relative to the atomic lattice and whether the electric field is parallel or antiparallel to B. The direction of the spin z-component is reversed by flipping the direction of the electric field. We provide several examples to explain the origin of this exquisite control.   

Mapping hole spin texture in quantum dots and quantum dot molecules

Holes in semiconductor quantum dots (QD) and quantum dot molecules (QDM) have unique electronic and spin properties that make them a promising candidate for a qubit. To understand the physical origin of these properties and identify promising paths to optimizing these properties for device applications, we use atomistic tight binding theory and a finite basis matrix approximation to compute the contributions to hole spin projections at each atomic site within a QD or QDM. We consider strained InAs/GaAs and strain-free GaAs/AlAs QDs and vertically stacked InAs/GaAs QDMs subject to a variety of applied electric and magnetic fields. For example, in a single GaAs/AlAs QD we observe a strong spin polarization in the z-direction with an applied lateral electric field parallel to a Voigt configuration magnetic field. However, the hole spin remains unpolarized when the lateral electric field is orthogonal to the magnetic field. We use a 3-D model to explore the spin contributions from anion and cation sites, different atomic planes, and separate QDs within a QDM. We suggest possible experiments to validate these computational results.   

Hole spins in quantum dot molecules: control with random alloy GaBiAs barriers

Quantum dot molecules (QDM) created by vertically stacking two semiconductor quantum dots (QD) have a tunneling barrier between the two dots which can be used to control hole spin, providing a promising candidate for qubits and qubit control. Interdot barriers of low Bi concentration GaBiAs can provide enhanced control of hole spins, by lowering the tunneling barrier for the holes without affecting conduction electrons or split off bands. We use atomistic tight-binding theory for InAs QDMs surrounded by an interdot barrier of GaAs with a GaBiAs layer inserted between the QDs, treating the GaBiAs as a random alloy in order to probe how the configurations of Bi atoms affect the overall behavior of the holes. We present results for electron and hole energies, as well as g-factor modification under applied vertical electric field, and hole spin-mixing to demonstrate how the thickness, location and Bi concentration of the GaBiAs layer modifies hole-spin physics in QDMs. We contrast the results obtained here for a GaBiAs layer treated as a random alloy with previous results obtained with a virtual crystal approximation for GaBiAs. We also discuss the sensitivity of the hole spin-mixing to different realizations of the random alloy.