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...

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.

Junctions consisting of two crossed single-walled carbon nanotubes were fabricated with electrical contacts at each end of each nanotube. The individual nanotubes were identified as metallic (M) or semiconducting (S), based on their two-terminal conductances; MM, MS, and SS four-terminal devices were studied. The MM and SS junctions had high conductances, on the order of 0.1 e(2)/h (where e is the electron charge and h is Planck's constant). For an MS junction, the semiconducting nanotube was depleted at the junction by the metallic nanotube, forming a rectifying Schottky barrier. We used two- and three-terminal experiments to fully characterize this junction.

Light management is of great importance in photovoltaic cells, as it determines the fraction of incident light entering the device. An optimal p-n junction combined with optimal light absorption can lead to a solar cell efficiency above the Shockley-Queisser limit. Here, we show how this is possible by studying photocurrent generation for a single core-shell p-i-n junction GaAs nanowire solar cell grown on a silicon substrate. At 1 sun illumination, a short-circuit current of 180 mA cm -2 is obtained, which is more than one order of magnitude higher than that predicted from the Lambert-Beer law. The enhanced light absorption is shown to be due to a light-concentrating property of the standing nanowire, as shown by photocurrent maps of the device. The results imply new limits for the maximum efficiency obtainable with III-V based nanowire solar cells under 1 sun illumination.N anowire-based solar cells hold great promise for third-generation photovoltaics and for powering nanoscale devices 1,2 . With the advent of third-generation photovoltaics, solar cells will become cheaper and more efficient than current devices. In particular, a cost reduction may be achieved by reducing material use through the fabrication of nanowire arrays and radial p-n junctions [3][4][5] . The geometry of nanowire crystals is expected to favour elastic strain relaxation, providing great freedom in the design of new compositional multijunction solar cells 6 grown on mismatched materials 7,8 . The efficiencies of nanostructured solar cells have increased over time and have now reached up to 13.8%, due to improvements in materials and new device concepts [9][10][11][12][13][14] .Light absorption in standing nanowires is a complex phenomenon, with a strong dependence on nanowire dimensions and the absorption coefficient of the raw materials [15][16][17][18] . In low-absorbing microwire arrays, such as those composed of silicon, light absorption is understood via ray optics or by calculation of the integrated local density of optical states of the nanowire film 19,20 . Interestingly, when these arrays stand on a Lambertian back-reflector, an asymptotic increase in light trapping for low filling factors (FFs) is predicted 19 . This is advantageous for improvement of the efficiency-to-cost ratio of solar cells and has led to the demonstration of microwire arrays exhibiting higher absorption than in the equivalent thickness of textured film 19,21,22 . The case for nanowires is quite different. Nanowire diameters are smaller than or comparable to the radiation wavelength. In this case, optical interference and guiding effects play a dominant role in relation to reflectivity and absorption spectra. For low-absorbing materials (for example, indirect bandgap materials such as silicon), waveguiding effects plays a key role 23,24 , whereas highly absorbing semiconductors (such as direct-bandgap GaAs) exhibit resonances that increase the total absorption several times. Nanowires lying on a substrate also exhibit such resonances, often described by Mi...

The connection of electrical leads to wire-like molecules is a logical step in the development of molecular electronics, but also allows studies of fundamental physics. For example, metallic carbon nanotubes are quantum wires that have been found to act as one-dimensional quantum dots, Luttinger liquids, proximity-induced superconductors and ballistic and diffusive one-dimensional metals. Here we report that electrically contacted single-walled carbon nanotubes can serve as powerful probes of Kondo physics, demonstrating the universality of the Kondo effect. Arising in the prototypical case from the interaction between a localized impurity magnetic moment and delocalized electrons in a metallic host, the Kondo effect has been used to explain enhanced low-temperature scattering from magnetic impurities in metals, and also occurs in transport through semiconductor quantum dots. The far greater tunability of dots (in our case, nanotubes) compared with atomic impurities renders new classes of Kondo-like effects accessible. Our nanotube devices differ from previous systems in which Kondo effects have been observed, in that they are one-dimensional quantum dots with three-dimensional metal (gold) reservoirs. This allows us to observe Kondo resonances for very large electron numbers (N) in the dot, and approaching the unitary limit (where the transmission reaches its maximum possible value). Moreover, we detect a previously unobserved Kondo effect, occurring for even values of N in a magnetic field.

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.

Non-locality is a fundamental property of quantum mechanics that manifests itself as correlations between spatially separated parts of a quantum system. A fundamental route for the exploration of such phenomena is the generation of Einstein-Podolsky-Rosen (EPR) pairs of quantum-entangled objects for the test of so-called Bell inequalities. Whereas such experimental tests of non-locality have been successfully conducted with pairwise entangled photons, it has not yet been possible to realize an electronic analogue of it in the solid state, where spin-1/2 mobile electrons are the natural quantum objects. The difficulty stems from the fact that electrons are immersed in a macroscopic ground state-the Fermi sea-which prevents the straightforward generation and splitting of entangled pairs of electrons on demand. A superconductor, however, could act as a source of EPR pairs of electrons, because its ground-state is composed of Cooper pairs in a spin-singlet state. These Cooper pairs can be extracted from a superconductor by tunnelling, but, to obtain an efficient EPR source of entangled electrons, the splitting of the Cooper pairs into separate electrons has to be enforced. This can be achieved by having the electrons 'repel' each other by Coulomb interaction. Controlled Cooper pair splitting can thereby be realized by coupling of the superconductor to two normal metal drain contacts by means of individually tunable quantum dots. Here we demonstrate the first experimental realization of such a tunable Cooper pair splitter, which shows a surprisingly high efficiency. Our findings open a route towards a first test of the EPR paradox and Bell inequalities in the solid state.

Many present and future applications of superconductivity would benefit from electrostatic control of carrier density and tunnelling rates, the hallmark of semiconductor devices. One particularly exciting application is the realization of topological superconductivity as a basis for quantum information processing. Proposals in this direction based on the proximity effect in semiconductor nanowires are appealing because the key ingredients are currently in hand. However, previous instances of proximitized semiconductors show significant tunnelling conductance below the superconducting gap, suggesting a continuum of subgap states--a situation that nullifies topological protection. Here, we report a hard superconducting gap induced by the proximity effect in a semiconductor, using epitaxial InAs-Al semiconductor-superconductor nanowires. The hard gap, together with favourable material properties and gate-tunability, makes this new hybrid system attractive for a number of applications, as well as fundamental studies of mesoscopic superconductivity.