Majorana zero modes are quasiparticle excitations in condensed matter systems that have been proposed as building blocks of fault-tolerant quantum computers [1]. They are expected to exhibit non-Abelian particle statistics, in contrast to the usual statistics of fermions and bosons, enabling quantum operations to be performed by braiding isolated modes around one another [1, 2]. Quantum braiding operations are topologically protected insofar as these modes are pinned near zero energy, and the pinning is predicted to be exponential as the modes become spatially separated [3, 4]. Following theoretical proposals [5, 6], several experiments have identified signatures of Majorana modes in proximitized nanowires [7][8][9][10][11] and atomic chains [12], with small modesplitting potentially explained by hybridization of Majoranas [13][14][15]. Here, we use Coulombblockade spectroscopy in an InAs nanowire segment with epitaxial aluminum, which forms a proximity-induced superconducting Coulomb island (a Majorana island) that is isolated from normal-metal leads by tunnel barriers, to measure the splitting of near-zero-energy Majorana modes. We observe exponential suppression of energy splitting with increasing wire length. For short devices of a few hundred nanometers, subgap state energies oscillate as the magnetic field is varied, as is expected for hybridized Majorana modes. Splitting decreases by a factor of about ten for each half a micrometer of increased wire length. For devices longer than about one micrometer, transport in strong magnetic fields occurs through a zero-energy state that is energetically isolated from a continuum, yielding uniformly spaced Coulomb-blockade conductance peaks, consistent with teleportation via Majorana modes [16, 17]. Our results help to explain the trivial-to-topological transition in finite systems and to quantify the scaling of topological protection with end-mode separation.The set of structures we investigate consist of InAs nanowires grown by molecular beam epitaxy in the [0001] wurtzite direction with an epitaxial Al shell on two facets of the hexagonal cross section [18]. The Al shell was removed except in a small segment of length L and isolated from normal metal (Ti/Au) leads by electrostatic gatecontrolled barriers (Fig. 1a). Charging energy, E C , of the device ranges from greater than to less than the superconducting gap of Al (∼ 0.2 meV). The thin Al shell (8 − 10 nm thickness on the two facets) gives a large critical field, B c , before superconductivity is destroyed: for fields along the wire axis, B c,|| ∼ 1 T; out of the plane of the substrate but roughly in the plane of the two Alcovered facets, B c,⊥ ∼ 700 mT (Fig. 1b). The very high achieved critical fields make these wires a suitable platform for investigating topological superconductivity [18].Five devices over a range of Al shell lengths L ∼ 0.3 − 1.5 µm were measured (see Methods for device layouts). Charge occupation and tunnel coupling to the leads were tuned via electrostatic gates. Differential conductan...

Controlling the properties of semiconductor/metal interfaces is a powerful method for designing functionality and improving the performance of electrical devices. Recently semiconductor/superconductor hybrids have appeared as an important example where the atomic scale uniformity of the interface plays a key role in determining the quality of the induced superconducting gap. Here we present epitaxial growth of semiconductor-metal core-shell nanowires by molecular beam epitaxy, a method that provides a conceptually new route to controlled electrical contacting of nanostructures and the design of devices for specialized applications such as topological and gate-controlled superconducting electronics. Our materials of choice, InAs/Al grown with epitaxially matched single-plane interfaces, and alternative semiconductor/metal combinations allowing epitaxial interface matching in nanowires are discussed. We formulate the grain growth kinetics of the metal phase in general terms of continuum parameters and bicrystal symmetries. The method realizes the ultimate limit of uniform interfaces and seems to solve the soft-gap problem in superconducting hybrid structures.

Au free GaAs nanowires with zinc blende structure, free of twin planes and with remarkable aspect ratios, have been grown on (111) Si substrates by molecular beam epitaxy. Nanowires with diameters down to 20 nm are obtained using a thin native oxide layer on the Si substrates. We discuss how the structural phase distribution along the wire length is controlled by the effective V/III ratio and temperature at the growth interface and explain how to obtain a pure twin plane free zinc blende structure.

Nanowire (NW) crystal growth via the vapour-liquid-solid mechanism is a complex dynamic process involving interactions between many atoms of various thermodynamic states. With increasing speed over the last few decades many works have reported on various aspects of the growth mechanisms, both experimentally and theoretically. We will here propose a general continuum formalism for growth kinetics based on thermodynamic parameters and transition state kinetics. We use the formalism together with key elements of recent research to present a more overall treatment of III-V NW growth, which can serve as a basis to model and understand the dynamical mechanisms in terms of the basic control parameters, temperature and pressures/beam fluxes. Self-catalysed GaAs NW growth on Si substrates by molecular beam epitaxy is used as a model system.

The perspectives offered by vertical arrays of nanowires for biosensing applications in living cells depend on the access of individual nanowires to the cell interior. Recent results on electrical access and molecular delivery suggest that direct access is not always obtained. Here, we present a generic approach to directly visualize the membrane conformation of living cells interfaced with nanowire arrays, with single nanowire resolution. The method combines confocal z-stack imaging with an optimized cell membrane labelling strategy which was applied to HEK293 cells interfaced with 2-11 μm long and 3-7 μm spaced nanowires with various surface coatings (bare, aminosilane-coated or polyethyleneimine-coated indium arsenide). We demonstrate that, for all commonly used nanowire lengths, spacings and surface coatings, nanowires generally remain enclosed in a membrane compartment, and are thereby not in direct contact with the cell interior.

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Cooper pair splitting (CPS) is a process in which the electrons of the naturally occurring spin-singlet pairs in a superconductor are spatially separated using two quantum dots. Here, we investigate the evolution of the conductance correlations in an InAs CPS device in the presence of an external magnetic field. In our experiments the gate dependence of the signal that depends on both quantum dots continuously evolves from a slightly asymmetric Lorentzian to a strongly asymmetric Fano-type resonance with increasing field. These experiments can be understood in a simple three-site model, which shows that the nonlocal CPS leads to symmetric line shapes, while the local transport processes can exhibit an asymmetric shape due to quantum interference. These findings demonstrate that the electrons from a Cooper pair splitter can propagate coherently after their emission from the superconductor and how a magnetic field can be used to optimize the performance of a CPS device. In addition, the model calculations suggest that the estimate of the CPS efficiency in the experiments is a lower bound for the actual efficiency. In the Cooper pair splitting (CPS) process the electrons of the Cooper pairs in a superconductor are separated spatially using two quantum dots (QDs) coupled in parallel to a central superconductor contact (S) in a three-terminal geometry [1-3], see Fig. 1(a). The Coulomb repulsion on the QDs and the quasiparticle energy gap of the superconductor enforce the electrons to separate into different normal metal electrodes (N1 and N2). Since Cooper pairs are spin-singlet states, such devices could serve as a source of nonlocal spin entangled electron pairs. Similar geometries are also relevant in the search for Majorana bound states [4] in local S-N junction experiments and in threeterminal devices, where an increase in CPS efficiency might serve as a signature of the elusive exotic states [5].In a series of recent experiments on semiconducting nanowires (NWs) [6][7][8][9], carbon nanotubes [10-12], and graphene [13], CPS was demonstrated by positive conductance correlations between the currents from S into N1 and N2. In these experiments, external magnetic fields were solely used to suppress the superconductivity for control experiments, but not as a parameter to tune CPS. In addition, most experiments were interpreted in terms of an incoherent picture with independent transport mechanisms, only coupled by the QD dynamics [9,11].Here, we report experiments in a NW-based Cooper pair splitter with a Nb superconducting electrode. The large critical magnetic field of Nb allows us to explore CPS up to ∼1 T. We find that the conductance correlations can not only manifest as symmetric peaks and dips in the gate dependence, but also as strongly asymmetric shapes reminiscent of Fano resonances. We interpret the experimental results in a minimal model that incorporates the superconducting proximity effect, the tunnel coupling between the QDs, and quantum interference [see Fig. 1(b)]. Interference results in asymmetric...

We present transport spectroscopy of sub-gap states in a bottom gated InAs nanowire coupled to a normal lead and a superconducting aluminium lead. The device shows clearly resolved subgap states which we can track as the coupling parameters of the system are tuned and as the gap is closed by means of a magnetic field. We systematically extract system parameters by using numerical renormalization group theory fits as a level of the quantum dot is tuned through a quantum phase transition electrostatically and magnetically. We also give an intuitive description of sub-gap excitations.