Hybrid nanowires combining semiconductor and superconductor materials appear well suited for the creation, detection, and control of Majorana bound states (MBSs). We demonstrate the emergence of MBSs from coalescing Andreev bound states (ABSs) in a hybrid InAs nanowire with epitaxial Al, using a quantum dot at the end of the nanowire as a spectrometer. Electrostatic gating tuned the nanowire density to a regime of one or a few ABSs. In an applied axial magnetic field, a topological phase emerges in which ABSs move to zero energy and remain there, forming MBSs. We observed hybridization of the MBS with the end-dot bound state, which is in agreement with a numerical model. The ABS/MBS spectra provide parameters that are useful for understanding topological superconductivity in this system.

We introduce a scheme for preparation, manipulation, and read out of Majorana zero modes in semiconducting wires with mesoscopic superconducting islands. Our approach synthesizes recent advances in materials growth with tools commonly used in quantum-dot experiments, including gate control of tunnel barriers and Coulomb effects, charge sensing, and charge pumping. We outline a sequence of milestones interpolating between zero-mode detection and quantum computing that includes (1) detection of fusion rules for non-Abelian anyons using either proximal charge sensors or pumped current, (2) validation of a prototype topological qubit, and (3) demonstration of non-Abelian statistics by braiding in a branched geometry. The first two milestones require only a single wire with two islands, and additionally enable sensitive measurements of the system's excitation gap, quasiparticle poisoning rates, residual Majorana zero-mode splittings, and topological-qubit coherence times. These pre-braiding experiments can be adapted to other manipulation and read out schemes as well.

We study electron transport in a double quantum dot in the Pauli spin blockade regime in the presence of strong spin-orbit coupling. The effect of spin-orbit coupling is incorporated into a modified interdot tunnel coupling. We elucidate the role of the external magnetic field, the nuclear fields in the dots, and the spin relaxation. We find qualitative agreement with experimental observations, and we propose a way to extend the range of magnetic fields in which blockade can be observed. DOI: 10.1103/PhysRevB.80.041301 PACS number͑s͒: 71.70.Ej, 73.63.Kv, 72.25.Ϫb Blockade phenomena, whereby strong interactions between single particles affect the global transport or excitation properties of a system, are widely used to control and detect quantum states of single particles. In single electron transistors, the electrostatic interaction between electrons can block the current flow, 1 thereby enabling precise control over the number of charges on the transistor.2 In semiconductor quantum dots, the Pauli exclusion principle can lead to a spinselective blockade, 3 which has proven to be a powerful tool for read-out of the spin degree of freedom of single electrons. [4][5][6][7][8] In this spin blockade regime, a double quantum dot is tuned such that current involves the transport cycle ͑0,1͒ → ͑1,1͒ → ͑0,2͒ → ͑0,1͒, ͑n , m͒ denoting a charge state with n͑m͒ excess electrons in the left͑right͒ dot ͓see Fig. 1͑a͔͒. Since the only accessible ͑0,2͒ state is a spin singlet, the current is blocked as soon as the system enters a ͑1,1͒ triplet state ͓Fig. 1͑b͔͒; transport is then due to spin relaxation processes, possibly including interaction with the nuclear fields. 9 This blockade has been used in GaAs quantum dots to detect coherent rotations of single electron spins, 4,5 coherent rotations of two-electron spin states, 6 and mixing of two-electron spin states due to hyperfine interaction with nuclear spins. 7,8 Motivated by a possibly large increase in efficiency of magnetic and electric control over the spin states, 10,11 also quantum dots in host materials with a relatively large g factor and strong spin-orbit interaction are being investigated. Very recently, Pauli spin blockade has been demonstrated in a double quantum dot defined by top gates along an InAs nanowire.12,13 However, as compared to GaAs, spin blockade in InAs nanowire quantum dots seems to be destroyed by the strong spin-orbit coupling: significant spin blockade has been only observed at very small external magnetic fields ͓Շ10 mT ͑Ref. 12͔͒. An important question is whether there exists a way to extend this interval of magnetic fields. To answer that question, one first has to understand the physical mechanism behind the lifting of the blockade.In this work we study Pauli spin blockade in the presence of strong spin-orbit mixing. We show that the only way spin-orbit coupling interferes with electron transport through a double dot is by introducing nonspin-conserving tunneling elements between the dots. This yields coupling of the ͑1,1͒ triplet states...

The main obstacle to coherent control of twolevel quantum systems is their coupling to an uncontrolled environment [1]. For electron spins in III-V quantum dots, the random environment is mostly given by the nuclear spins in the quantum dot host material; they collectively act on the electron spin through the hyperfine interaction, much like a random magnetic field [2, 3,4,5,6,7,8]. Here we show that the same hyperfine interaction can be harnessed such that partial control of the normally uncontrolled environment becomes possible. In particular, we observe that the electron spin resonance frequency remains locked to the frequency of an applied microwave magnetic field, even when the external magnetic field or the excitation frequency are changed. The nuclear field thereby adjusts itself such that the electron spin resonance condition remains satisfied. General theoretical arguments indicate that this spin resonance locking is accompanied by a significant reduction of the randomness in the nuclear field.In thermodynamic equilibrium, the nuclear spins in the quantum dot host material are randomly oriented, even at dilution refrigerator temperatures and in magnetic fields of a few Tesla. An electron spin confined in the quantum dot interacts via the hyperfine coupling with N ∼ 10 6 nuclear spins and as a result experiences a random nuclear field B N . This random nuclear field is sampled from a distribution with a root mean square width ∝ A/gµ B √ N , where g is the electron g-factor, µ B the Bohr magneton and A the hyperfine coupling constant (≈ 135µeV in GaAs). Measurements typically give a width of ∼ 1 mT. As a result, we lose track of the phase of a freely evolving electron spin within a time T * 2 of a few tens of nanoseconds [3,4,6,7,8]. Similarly, when the spin evolves under an oscillating driving field, the nuclear field leads to a random offset in the resonance condition which has a comparable amplitude to presently achievable driving fields. This results in poorly controlled spin rotations [9].It is therefore of great importance to develop the ability to control and manipulate the nuclear field with great precision. In particular, it would be highly desirable to set the nuclear field to a narrow distribution of values at the start of every experiment [10,11,12,13]. This would immediately reduce the rapid dephasing, and the electron spin would loose phase coherence only from the slow subsequent evolution of the nuclear field, giving a predicted spin coherence time of 1 − 10µs [14,15]. Such narrowing has been achieved in an ensemble of self-assembled quantum dots by synchronizing the precessing spins with a series of laser pulses [16]. More recently, the spread of the difference in nuclear fields in two neighbouring quantum dots was reduced via a gate voltage controlled pumping cycle, giving a 70-fold increase in the T * 2 for states in the two-electron m z = 0 subspace [17].Here we exploit electron-nuclear feedback in order to control and manipulate the nuclear fields in two coupled quantum dots during con...

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...

We investigate effects of quasiparticle poisoning in a Majorana island with strong tunnel coupling to normal-metal leads. In addition to the main Coulomb blockade diamonds, "shadow" diamonds appear, shifted by 1e in gate voltage, consistent with transport through an excited (poisoned) state of the island. Comparison to a simple model yields an estimate of parity lifetime for the strongly coupled island (∼ 1 µs) and sets a bound for a weakly coupled island (> 10 µs). Fluctuations in the gate-voltage spacing of Coulomb peaks at high field, reflecting Majorana hybridization, are enhanced by the reduced lever arm at strong coupling. In energy units, fluctuations are consistent with previous measurements.Hybrid semiconductor-superconductor nanowire devices have been the focus of intense research in recent years [1-6] primarily because they are expected to support Majorana zero modes [7,8]. Of particular relevance to schemes for Majorana fusion-rule testing, braiding, and Majorana-based quantum computation [9][10][11][12] is the Majorana island geometry, in which the topological hybrid nanowire acquires a charging energy that lifts the degeneracy between occupied and empty Majorana states [6,[13][14][15][16], allowing for charge readout of the state parity.A fundamental bound to the coherence of Majorana based qubits is the parity lifetime of the Majorana state, limited by quasiparticle poisoning [9,17,18]. Studies on metallic superconductors have explored the associated poisoning rates in great detail [19][20][21][22][23][24][25][26][27][28], while experiments on semiconductor-superconductor hybrids have only established bounds on the relaxation rate of quasiparticles into the subgap state [29], with quantitative estimates for poisoning from external sources still pending.In this Letter, we use Coulomb blockade spectroscopy to quantify the quasiparticle poisoning time of a Majorana island. We find the poisoning time to a state with one extra quasiparticle in the BCS continuum to be ∼ 1 µs in the regime of relatively strong coupling between the island and the leads, and bounded from below by 10 µs in the less strongly coupled regime investigated in Ref. [29]. Our results demonstrate transport signatures of quasiparticle poisoning in Majorana islands up to the topological phase transition and place constraints on a relevant timescale for topological quantum computation and Majorana braiding.The device we investigate consisted of an MBE-grown [0001] wurtzite InAs nanowire with epitaxial Al on two of six facets [ Fig. 1(a)], which induces a hard superconducing gap in the nanowire [30,31]. The Al shell was removed on both ends using a chemical etch, leaving an Al island of length L ∼ 400 nm. Uncovered InAs segments at the wire ends are electrically contacted using normal-metal (Ti/Au) ohmic contacts. Lithographically patterned electrostatic gates near the ∼ 50 nm exposed segments next to the ohmic contacts were used to deplete carriers, bringing the device into the Coulomb blockade regime. Magnetic fields were applied per...

Two-terminal conductance spectroscopy of superconducting devices is a common tool for probing Andreev and Majorana bound states. Here, we study theoretically a three-terminal setup, with two normal leads coupled to a grounded superconducting terminal. Using a single-electron scattering matrix, we derive the subgap conductance matrix for the normal leads and discuss its symmetries. In particular, we show that the local and the nonlocal elements of the conductance matrix have pairwise identical antisymmetric components. Moreover, we find that the nonlocal elements are directly related to the local BCS charges of the bound states close to the normal probes and we show how the BCS charge of overlapping Majorana bound states can be extracted from experiments. arXiv:1905.05438v1 [cond-mat.mes-hall]

We investigate patterns of critical current as a function of perpendicular and in-plane magnetic fields in superconductor-semiconductor-superconductor (SNS) junctions based on InAs/InGaAs heterostructures with an epitaxial Al layer. This material system is of interest due to its exceptionally good superconductor-semiconductor coupling, as well as large spin-orbit interaction and g-factor in the semiconductor. Thin epitaxial Al allows the application of large in-plane field without destroying superconductivity. For fields perpendicular to the junction, flux focusing results in aperiodic node spacings in the pattern of critical currents known as Fraunhofer patterns by analogy to the related interference effect in optics. Adding an in-plane field yields two further anomalies in the pattern. First, higher order nodes are systematically strengthened, indicating current flow along the edges of the device, as a result of confinement of Andreev states driven by an induced flux dipole; second, asymmetries in the interference appear that depend on the field direction and magnitude. A model is presented, showing good agreement with experiment, elucidating the roles of flux focusing, Zeeman and spin-orbit coupling, and disorder in producing these effects.