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.

Realizing topological superconductivity and Majorana zero modes in the laboratory is one of the major goals in condensed matter physics. We review the current status of this rapidly-developing field, focusing on semiconductor-superconductor proposals for topological superconductivity. Material science progress and robust signatures of Majorana zero modes in recent experiments are discussed. After a brief introduction to the subject, we outline several next-generation experiments probing exotic properties of Majorana zero modes, including fusion rules and non-Abelian exchange statistics. Finally, we discuss prospects for implementing Majorana-based topological quantum computation in these systems.

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...

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.