We study theoretically the low-energy hole states of Ge/Si core/shell nanowires. The low-energy valence band is quasi-degenerate, formed by two doublets of different orbital angular momentum, and can be controlled via the relative shell thickness and via external fields. We find that direct (dipolar) coupling to a moderate electric field leads to an unusually large spin-orbit interaction of Rashba-type on the order of meV which gives rise to pronounced helical states enabling electrical spin-control. The system allows for quantum dots and spin-qubits with energy levels that can vary from nearly zero to several meV, depending on the relative shell thickness.

Experimental and theoretical progress toward quantum computation with spins in quantum dots (QDs) is reviewed, with particular focus on QDs formed in GaAs heterostructures, on nanowire-based QDs, and on self-assembled QDs. We report on a remarkable evolution of the field where decoherence -one of the main challenges for realizing quantum computers -no longer seems to be the stumbling block it had originally been considered. General concepts, relevant quantities, and basic requirements for spin-based quantum computing are explained; opportunities and challenges of spin-orbit interaction and nuclear spins are reviewed. We discuss recent achievements, present current theoretical proposals, and make several suggestions for further experiments.

We study theoretically the low-energy hole states in Si, Ge, and Ge/Si core/shell nanowires (NWs). The NW core in our model has a rectangular cross section, the results for a square cross section are presented in detail. In the case of Ge and Ge/Si core/shell NWs, we obtain very good agreement with previous theoretical results for cylindrically symmetric NWs. In particular, the NWs allow for an unusually strong and electrically controllable spin-orbit interaction (SOI) of Rashba type. We find that the dominant contribution to the SOI is the "direct Rashba spin-orbit interaction" (DRSOI), which is an important mechanism for systems with heavy-hole-lighthole mixing. Our results for Si NWs depend significantly on the orientation of the crystallographic axes. The numerically observed dependence on the growth direction is consistent with analytical results from a simple model, and we identify a setup where the DRSOI enables spin-orbit energies of the order of millielectronvolts in Si NWs. Furthermore, we analyze the dependence of the SOI on the electric field and the cross section of the Ge or Si core. A helical gap in the spectrum can be opened with a magnetic field. We obtain the largest g factors with magnetic fields applied perpendicularly to the NWs. arXiv:1712.03476v1 [cond-mat.mes-hall]

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We propose a setup for universal and electrically controlled quantum information processing with hole spins in Ge/Si core/shell nanowire quantum dots (NW QDs). Single-qubit gates can be driven through electric-dipoleinduced spin resonance, with spin-flip times shorter than 100 ps. Long-distance qubit-qubit coupling can be mediated by the cavity electric field of a superconducting transmission line resonator, where we show that operation times below 20 ns seem feasible for the entangling √ iSWAP gate. The absence of Dresselhaus spinorbit interaction (SOI) and the presence of an unusually strong Rashba-type SOI enable precise control over the transverse qubit coupling via an externally applied, perpendicular electric field. The latter serves as an on-off switch for quantum gates and also provides control over the g factor, so single-and two-qubit gates can be operated independently. Remarkably, we find that idle qubits are insensitive to charge noise and phonons, and we discuss strategies for enhancing noise-limited gate fidelities. PACS numbers: 73.21.Hb, 73.21.La, 42.50.Pq, 03.67.Lx In the past decade, the idea of processing quantum information with spins in quantum dots (QDs) [1] was followed by remarkable progress [2]. While the workhorse systems are highly advanced, such as self-assembled (In)GaAs QDs [3-10] and negatively charged, lateral GaAs QDs [11][12][13][14][15][16][17], an emerging theme is the search for systems that allow further optimization. In particular, Ge and Si have attracted attention because they can be grown nuclear-spin-free, which eliminates a major source of decoherence [18][19][20] Prime examples for novel qubits are hole spins in Ge/Si NW QDs [25, 26, 31,42,48], because they combine all the advantages of group-IV materials, VB states, and strong confinement along two axes. The Si shell provides a large VB offset ∼0.5 eV [22], induces strain, and removes dangling bonds from the core. Furthermore, the holes feature an unusually strong Rashba-type spin-orbit interaction (SOI), referred to as direct Rashba SOI (DRSOI), that is not suppressed by the band gap [48]. We show here that these properties are highly useful for implementing spin qubits.In this work, we propose a setup for quantum information processing with holes in Ge/Si core/shell NW QDs. In stark contrast to previous systems [13,[43][44][45][46][47]49], where the EDSR relies on conventional Dresselhaus and Rashba SOI [50], the dynamics in our setup are governed by the DRSOI whose origin fundamentally differs. We find that EDSR allows flipping of hole spins within less than 100 ps. Two-qubit gates can be realized via circuit quantum electrodynamics (CQED), i.e., with an on-chip cavity [51][52][53], where we estimate that operation times below 20 ns are feasible for √ iSWAP. The long-range spin-spin interactions [49,[54][55][56] enable upscaling. Compared to the original proposal for electron spins in InAs [49], which was recently followed by encouraging results [46], we find several new and striking features. First, because o...

We theoretically consider g factor and spin lifetimes of holes in a longitudinal Ge/Si core/shell nanowire quantum dot that is exposed to external magnetic and electric fields. For the ground states, we find a large anisotropy of the g factor which is highly tunable by applying electric fields. This tunability depends strongly on the direction of the electric field with respect to the magnetic field. We calculate the single-phonon hole spin relaxation times T1 for zero and small electric fields and propose an optimal setup in which very large T1 of the order of tens of milliseconds can be reached. Increasing the relative shell thickness or the longitudinal confinement length further prolongs T1. In the absence of electric fields, the dephasing vanishes and the decoherence time T2 is determined by T2 = 2T1.PACS numbers: 71.70. Ej, 81.07.Vb, 81.07.Ta Semiconducting nanowires (NWs) allow to create nanoscale systems defined precisely regarding composition, geometry, and electronic properties and hence are subject to great experimental efforts. Furthermore, they offer new ways for implementing spin-based quantum computation.1 Both III-V compounds and group-IV materials are considered and operated in the conduction band (CB, electrons) 2-9 and in the valence band (VB, holes)10-22 regime. A particularly favored material is InAs, where single-electron quantum dots (QDs) 3 and electrically controlled spin rotations 5,6,8 have been implemented. Recently, qubits have also been implemented in InSb NW QDs, 7,9,22 a system for which extremely large electron g factors have been found. 4,7 However, the strong hyperfine interaction in InAs and InSb is considered the dominant source for the short coherence times observed.5,9 The latter may therefore be substantially prolonged in group-IV NWs that can be grown nuclearspin-free. In this context, Ge and Si have emerged as promising materials for nanoscale systems such as lateral QDs, 23-26 self-assembled QDs, 27-29 cylindrical core/shell NWs, 10-20 and ultrathin, triangular NWs. 21For applications in spintronics and quantum information processing, it can be advantageous to consider holes instead of electrons. Due to the p-wave symmetry of the Bloch states, holes experience a strong spin-orbit interaction (SOI) on the atomic level leading to an effective spin J = 3/2 behavior. Hence spin and momentum are coupled strongly which allows efficient control of the hole spin by electrical means. Furthermore, hole spin lifetimes are prolonged in the presence of confinement. 30-35In Ge/Si core/shell NWs, the large VB offset leads to an accumulation of holes in the core.11,36 They form a one dimensional (1D) hole gas with an unusually large, tunable Rashba-type SOI, referred to as direct Rashba SOI (DRSOI).37 This DRSOI makes Ge/Si core/shell NWs attractive candidates for quantum information processing via electric-dipole induced spin resonance, 38 and we mention that signatures of a tunable Rashba SOI were already deduced from magnetotransport experiments. 17Experiments on gate defined QDs...

Hole spins have gained considerable interest in the past few years due to their potential for fast electrically controlled qubits. Here, we study holes confined in Ge hut wires, a so-far unexplored type of nanostructure. Low-temperature magnetotransport measurements reveal a large anisotropy between the in-plane and out-of-plane g-factors of up to 18. Numerical simulations verify that this large anisotropy originates from a confined wave function of heavy-hole character. A light-hole admixture of less than 1% is estimated for the states of lowest energy, leading to a surprisingly large reduction of the out-of-plane g-factors compared with those for pure heavy holes. Given this tiny light-hole contribution, the spin lifetimes are expected to be very long, even in isotopically nonpurified samples.

We study theoretically the phonon-induced relaxation (T1) and decoherence times (T2) of singlet-triplet qubits in lateral GaAs double quantum dots (DQDs). When the DQD is biased, Pauli exclusion enables strong dephasing via two-phonon processes. This mechanism requires neither hyperfine nor spin-orbit interaction and yields T2 T1, in contrast to previous calculations of phonon-limited lifetimes. When the DQD is unbiased, we find T22T1 and much longer lifetimes than in the biased DQD. For typical setups, the decoherence and relaxation rates due to one-phonon processes are proportional to the temperature T , whereas the rates due to two-phonon processes reveal a transition from T 2 to higher powers as T is decreased. Remarkably, both T1 and T2 exhibit a maximum when the external magnetic field is applied along a certain axis within the plane of the two-dimensional electron gas. We compare our results with recent experiments and analyze the dependence of T1 and T2 on system properties such as the detuning, the spin-orbit parameters, the hyperfine coupling, and the orientation of the DQD and the applied magnetic field with respect to the main crystallographic axes.