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.

We study theoretically electron spins in nanowire quantum dots placed inside a transmission line resonator. Because of the spin-orbit interaction, the spins couple to the electric component of the resonator electromagnetic field and enable coherent manipulation, storage, and read-out of quantum information in an all-electrical fashion. Coupling between distant quantum-dot spins, in one and the same or different nanowires, can be efficiently performed via the resonator mode either in real time or through virtual processes. For the latter case we derive an effective spin-entangling interaction and suggest means to turn it on and off. We consider both transverse and longitudinal types of nanowire quantum-dots and compare their manipulation timescales against the spin relaxation times. For this, we evaluate the rates for spin relaxation induced by the nanowire vibrations (phonons) and show that, as a result of phonon confinement in the nanowire, this rate is a strongly varying function of the spin operation frequency and thus can be drastically reduced compared to lateral quantum dots in GaAs. Our scheme is a step forward to the formation of hybrid structures where qubits of different nature can be integrated in a single device.

We study the triangular antiferromagnet Cu3 in external electric fields, using symmetry group arguments and a Hubbard model approach. We identify a spin-electric coupling caused by an interplay between spin exchange, spin-orbit interaction, and the chirality of the underlying spin texture of the molecular magnet. This coupling allows for the electric control of the spin (qubit) states, e.g. by using an STM tip or a microwave cavity. We propose an experimental test for identifying molecular magnets exhibiting spin-electric effects. [5,6,7], or the decoherence and the transition from quantum to classical behavior [8]. SMMs with antiferromagnetic coupling between neighboring spins are especially promising for the encoding and manipulation of quantum information [9,10,11,12], for they act as effective two-level systems, while providing additional auxiliary states that can be exploited for performing quantum gates, even in the presence of untunable couplings between the qubits [13]. Intra-and inter-molecular couplings of SMMs can be engineered by molecular and supra-molecular chemistry [14], enabling a bottom-up design of molecule-based devices [15].While the properties of SMMs can be modfied during the synthesis, control on the time scales required for quantum information processing remains a challenge. The standard spin-control technique is electron spin resonance (ESR) driven by ac magnetic fields B ac (t) [8,16,17,18]. For manipulation on the time scale of 1 ns (Rabi frequency Ω R ∼ 10 9 s −1 ) B ac should be of the order of 10 −2 T, which, however, is difficult to achieve. The spatial resolution of 1 nm, required for addressing a single molecule, is also prohibitively small. At these spatial and temporal scales, the electric control is preferable, because strong electric fields can be applied to small regions by using, for example, STM tips [19,20,21]. Also, the quantized electric field inside a microwave cavity can be used [22,23,24,25] to control single qubits and to induce coupling between them even if they are far apart.Here we identify and study an efficient spin-electric coupling mechanism in SMMs which is based on an interplay of spin exchange, spin-orbit interaction (SOI), and lack of inversion symmetry. Spin-electric effects induced solely by SOI [26] have been proposed [27] and experimentally demonstrated [28] in quantum dots. However, these SOI effects scale with the system size L as L 3 [27], making them irrelevant for the much smaller SMMs. Thus, additional ingredients-such as broken symmetriesmust be present in SMMs for an efficient coupling between spin and applied electric field.In the following, we demonstrate the possibility of such spin-electric effects in SMMs by focusing on a specific example, namely an equilateral spin triangle, Cu 3 [29]. In this SMM, the low energy states exhibit a chiral spin texture and, due to the absence of inversion symmetry, electric fields couple states of opposite chirality. Moreover, SOI couples the chirality to the total spin, and thus an effective spin-electri...

Just like insulators can present topological phases characterized by Dirac edge states, superconductors can exhibit topological phases characterized by Majorana edge states. In particular, one-dimensional topological superconductors are predicted to host zero-energy Majorana fermions at their extremities. By contrast, two-dimensional superconductors have a one-dimensional boundary which would naturally lead to propagating Majorana edge states characterized by a Dirac-like dispersion. In this paper we present evidences of one-dimensional dispersive in-gap edge states surrounding a two-dimensional topological superconducting domain consisting of a monolayer of Pb covering magnetic Co–Si islands grown on Si(111). We interpret the measured dispersive in-gap states as a spatial topological transition with a gap closure. Our method could in principle be generalized to a large variety of heterostructures combining a Rashba superconductor with a magnetic layer in order to be used as a platform for engineering topological quantum phases.