Majoranas Arrive When a negatively charged electron meets a positron—its positively charged antiparticle—they annihilate each other in a flash of gamma rays. A Majorana fermion, on the other hand, is a neutral particle, which is its own antiparticle. No sightings of a Majorana have been reported in the elementary particle world, but recently they have been proposed to exist in solid-state systems and suggested to be of interest as a quantum computing platform. Mourik et al. (p. 1003 , published online 12 April; see the cover; see the Perspective by Brouwer ) set up a semiconductor nanowire contacted on each end by a normal and a superconducting electrode that revealed evidence of Majorana fermions.

In 1984, Bychkov and Rashba introduced a simple form of spin-orbit coupling to explain the peculiarities of electron spin resonance in two-dimensional semiconductors. Over the past 30 years, Rashba spin-orbit coupling has inspired a vast number of predictions, discoveries and innovative concepts far beyond semiconductors. The past decade has been particularly creative, with the realizations of manipulating spin orientation by moving electrons in space, controlling electron trajectories using spin as a steering wheel, and the discovery of new topological classes of materials. This progress has reinvigorated the interest of physicists and materials scientists in the development of inversion asymmetric structures, ranging from layered graphene-like materials to cold atoms. This Review discusses relevant recent and ongoing realizations of Rashba physics in condensed matter.

Nanowires can serve as one-dimensional templates for scalable qubit registers. Unique to nanowires is the possibility to easily vary the material even during wire growth. 5Such flexibility can be used to design wires with suppressed decoherence and push semiconductor qubit fidelities towards error-correction levels. Furthermore, electrical dots can be integrated with optical dots in p-n junction nanowires. 6 The coherence times achieved here are sufficient for the conversion of an electronic qubit into a photon, the flying qubit, for long-distance quantum communication. Figure 1a shows a scanning electron microscope image of our nanowire device. Two electrodes, source and drain, are used to apply a voltage bias of 6 mV across the InAs nanowire. Voltages applied to five closely spaced narrow gates underneath the nanowire

Double quantum dot in the few-electron regime is achieved using local gating in an InSb nanowire. The spectrum of two-electron eigenstates is investigated using electric dipole spin resonance. Singlettriplet level repulsion caused by spin-orbit interaction is observed. The size and the anisotropy of singlet-triplet repulsion are used to determine the magnitude and the orientation of the spin-orbit effective field in an InSb nanowire double dot. The obtained results are confirmed using spin blockade leakage current anisotropy and transport spectroscopy of individual quantum dots.PACS numbers: 73.63. Kv, 85.35.Be The spin-orbit interaction (SOI) describes coupling between the motion of an electron and its spin. In one dimension, where electrons can move only to the left or to the right, the SOI couples this left or right motion to either spin-up or spin-down. An extreme situation occurs in what is called a helical liquid [1] where, in the presence of magnetic field, all spin-up electrons move to the left and all spin-down electrons to the right. As proposed recently [2,3], a helical liquid in proximity to a superconductor can generate Majorana fermions [4]. The search for Majorana fermions in 1D conductors is focused on finding the best material in terms of a strong spin-orbit interaction and large Landé g-factors. The latter is required for a helical liquid to exist at magnetic fields that do not suppress superconductivity. High g-factors of the order 50, strong SOI and the ability to induce superconductivity put forward InSb nanowires [5,6] as a natural platform for the realization of 1D topological states.The SOI can be expressed as an effective magnetic field B SO that depends on the electron momentum. An electron moving through the wire undergoes spin precession around B SO with a π rotation over a distance l SO called the spin-orbit length (see Fig. 1(a)). The length l SO is a direct measure of the SOI strength: a stronger SOI results in a shorter l SO . In this letter, we use spin spectra of single electrons in quantum dots [7] to extract l SO and the direction of B SO . In quantum dots, the SOI hybridizes states with different spin [5,8,9]. For a single electron, the SOI-hybridized spin-up and spin-down states form a spin-orbit qubit [10,11]. For two electrons SOI hybridization induces level repulsion between singlet and triplet states. The resulting level-repulsion gap between the well-defined qubit states can be used to measure the SOI: the gap size is determined by l SO [5,8,9] and the gap anisotropy indicates the direction of B SO [12][13][14]. Double quantum dots in InSb nanowires are defined by local gating (Figs. 1(b),1(c)). A finite voltage is applied across the source and drain electrodes; and the current through the nanowire is measured. Five gates underneath the wire create the confinement potential and control the electron number on the two dots [9,15]. We focus on the (1,1) charge configuration ( Fig. 1(d)), in which both the left and the right dot contain exactly one electron, each of them...

Ballistic one-dimensional transport in semiconductor nanowires plays a central role in creating topological and helical states. The hallmark of such one-dimensional transport is conductance quantization. Here we show conductance quantization in InSb nanowires at nonzero magnetic fields. Conductance plateaus are studied as a function of source-drain bias and magnetic field, enabling extraction of the Landég factor and the subband spacing. KEYWORDS:Conductance quantization, ballistic transport, quantum point contact, subband, nanowire, InSb S emiconductor nanowires are the starting point of recently proposed topological systems. 1−3 A topological superconducting region arises in a one-dimensional (1D) semiconductor wire in the presence of a strong spin−orbit coupling when it is brought in contact with a superconducting material. On the boundary of the topological and nontopological wire regions Majorana fermions (MFs) are expected. 4 The MFs in a nanowire, quasi-particles that are an equal superposition of an electron and a hole, are candidate building blocks for faulttolerant quantum computation. 4,5 Moreover, 1D semiconductor wires with strong spin−orbit coupling have also been identified as a suitable platform for creation of a helical state. 6−8 In such a state spin and momentum of an electron are perfectly correlated, thereby creating spin polarization and allowing spin filtering, key themes in the field of spintronics. 9−11 InSb nanowires, alongside InAs and Si/Ge core−shell nanowires, are promising for study of topological and helical states, as they have a strong spin−orbit interaction, 12 and superconductivity can be induced in the nanowires. 13 Indeed signatures of MFs have been reported in hybrid semiconductor−superconductor InSb nanowire devices. 14 While in InSb nanowires the basic properties of spin−orbit interaction and induced superconductivity have each been separately investigated, the degree of fulfillment of the third requirement for creation of MFs, the 1D semiconductor wire, is not as well understood. In a 1D wire transport takes place in subbands, of which the occupation is controlled by an external gate voltage. While first schemes for detection of MFs required occupation of only a single subband near the superconducting contacts where the MFs form, 1,2 later proposals extended this condition to the multisubband regime. 15−17 Information about the energy spectrum of InSb nanowires needed to answer questions of subband occupation is however lacking. Moreover, MFs are affected by disorder in the wire, 17−19 of which the extent is unknown. Such disorder creates diffusive transport, instead of the ballistic transport implied in the 1D requirement. Subband occupation and disorder are also key issues in creation of helical states in InSb nanowires.The formation of subbands in (ballistic) 1D wires is shown in transport measurements by quantization of conductance, where each spin-degenerate subband contributes a conductance of g Q = 2e 2 /h. 20,21 In semiconductor nanowires conductan...

We have achieved the few-electron regime in InAs nanowire double quantum dots. Spin blockade is observed for the first two half-filled orbitals, where the transport cycle is interrupted by forbidden transitions between triplet and singlet states. Partial lifting of spin blockade is explained by spin-orbit and hyperfine mechanisms that enable triplet to singlet transitions. The measurements over a wide range of interdot coupling and tunneling rates to the leads are well reproduced by a simple transport model. This allows us to separate and quantify the contributions of the spin-orbit and hyperfine interactions. DOI: 10.1103/PhysRevB.81.201305 PACS number͑s͒: 73.63.Kv, 71.70.Ej Spins in semiconductor quantum dots are possible building blocks for quantum information processing.1 The ultimate control of spin states is achieved in electrically defined single and double quantum dots.2 Many semiconductors that host such dots exhibit strong spin-orbit and hyperfine interactions. On the one hand, these interactions provide means of coherent spin control.3,4 On the other hand, they mix spin states. In double quantum dots, mixing of singlet and triplet states weakens spin blockade, 5-9 which is a crucial effect for spin-qubit operation. 10,11 Spin mixing due to hyperfine interaction was studied in GaAs double quantum dots, where spin-orbit coupling was weak. 5,6,12 In InAs, besides the hyperfine interaction, also spin-orbit interaction has a considerable effect on spin blockade. Previous measurement on many-electron double dots in InAs nanowires demonstrated that spin blockade is lifted by both interactions. 7,8 However, the effects of these two interactions could not be separated. As a consequence, the exact determination of the spin-orbit mechanism was lacking.In this Rapid Communication, we establish the individual roles of spin-orbit and hyperfine interactions in the spinblockade regime. Spin blockade is observed in tunable gatedefined few-electron double quantum dots in InAs nanowires. In the few-electron regime, the quantum states involved in transport can be reliably identified and the effects from excess electrons in the dots can be ruled out. This enables a careful comparison to theory which includes random nuclear magnetic fields as well as spin-orbit mediated tunneling between triplets and singlets. 13 The effects of the two interactions are traced in three distinct transport regimes, determined by the interdot coupling and the tunneling rates to the leads. The regimes are observed in two few-electron nanowire devices, results from one of them are discussed in this Rapid Communication.The nanowire devices are fabricated on prepatterned substrates, following Ref. 14 ͑Fig. 1, upper inset͒. The substrates are patterned with narrow metallic gates which are covered with a 20 nm layer of Si 3 N 4 dielectric to suppress gate leakage.15 Single-crystalline InAs nanowires with diameters from 40 to 80 nm are deposited randomly on the substrate. Conveniently aligned wires are contacted by source and drain electrodes. Si...

Due to the strong spin-orbit interaction in indium antimonide, orbital motion and spin are no longer separated. This enables fast manipulation of qubit states by means of microwave electric fields. We report Rabi oscillation frequencies exceeding 100 MHz for spin-orbit qubits in InSb nanowires. Individual qubits can be selectively addressed due to intrinsic differences in their gfactors. Based on Ramsey fringe measurements, we extract a coherence time T * 2 = 8 ± 1 ns at a driving frequency of 18.65 GHz. Applying a Hahn echo sequence extends this coherence time to 35 ns.The spin of a single electron forms a two-level system, which makes it a natural choice for creating a quantum bit (qubit) [1]. Quantum information processing based on such qubits has developed into a mature and diverse field [2]. Previous work has demonstrated important milestones, including single-shot detection of spin state, coherent control of a single spin and coherent coupling between two spins [2][3][4][5][6]. Of great importance for future development of spin-based quantum computation is combining efficient single-qubit control and two-qubit operations in the same system [7] and developing ways to integrate spin qubits with other quantum computing architectures. To pursue these goals, several promising material platforms are being explored. Among these are narrow band-gap semiconductor nanowires, such as indium arsenide and indium antimonide. This class of materials has recently gained considerable attention, due to their strong spin-orbit coupling, which enables efficient all-electrical spin control [5,[8][9][10][11] and could provide a means of coupling qubits to quantum systems based on superconducting cavities [12].In this paper we demonstrate an electrically controlled spin-orbit qubit in an indium antimonide nanowire. We observe Rabi oscillations with frequencies up to 104 MHz, the fastest reported to date for an electrically controlled single-spin qubit in a quantum dot. Furtermore, we show that the individual qubits in the two dots can be addressed with high selectivity, owing to a large g-factor difference between two dots. We achieve universal qubit control and study qubit coherence by means of Ramsey type measurements. We find that the inhomogeneous dephasing time T * 2 can be extended to ∼ 35 ns by using a Hahn echo.To realize our spin-orbit qubit, a double quantum dot is defined inside the nanowire by means of local electrostatic gating. The qubits' basis states are spin-orbit doublets (denoted by ⇑ and ⇓), which-analogous to conventional spin qubits-are split by the Zeeman energy in a magnetic field. Transitions between these states can be induced by applying microwave frequency electric fields.An image of our device obtained by scanning electron microscopy is presented in figure 1(a). It consists of an indium antimonide nanowire (∼ 1.5µm long, 100 nm thick) contacted by Ti/Al source and drain electrodes. Below the nanowire, separated by a layer of Si 3 N 4 dielectric, is a set of 5 narrow gates (60 nm pitch) used to induce...

High aspect ratios are highly desired to fully exploit the one-dimensional properties of indium antimonide nanowires.Here we systematically investigate the growth mechanisms and find parameters leading to long and thin nanowires. Variation of the V/III ratio and the nanowire density are found to have the same influence on the "local" growth conditions and can control the InSb shape from thin nanowires to nanocubes. We propose that the V/III ratio controls the droplet composition and the radial growth rate and these parameters determine the nanowire shape. A sweet spot is found for nanowire interdistances around 500 nm leading to aspect ratios up to 35. High electron mobilities up to 3.5 × 10 4 cm 2 V −1 s −1 enable the realization of complex spintronic and topological devices.