Selective-area growth is a promising technique for enabling of the fabrication of the scalable III–V nanowire networks required to test proposals for Majorana-based quantum computing devices. However, the contours of the growth parameter window resulting in selective growth remain undefined. Herein, we present a set of experimental techniques that unambiguously establish the parameter space window resulting in selective III–V nanowire networks growth by molecular beam epitaxy. Selectivity maps are constructed for both GaAs and InAs compounds based on in situ characterization of growth kinetics on GaAs(001) substrates, where the difference in group III adatom desorption rates between the III–V surface and the amorphous mask area is identified as the primary mechanism governing selectivity. The broad applicability of this method is demonstrated by the successful realization of high-quality InAs and GaAs nanowire networks on GaAs, InP, and InAs substrates of both (001) and (111)B orientations as well as homoepitaxial InSb nanowire networks. Finally, phase coherence in Aharonov–Bohm ring experiments validates the potential of these crystals for nanoelectronics and quantum transport applications. This work should enable faster and better nanoscale crystal engineering over a range of compound semiconductors for improved device performance.

The number of electrons in small metallic or semiconducting islands is quantised. When tunnelling is enabled via opaque barriers this number can change by an integer. In superconductors the addition is in units of two electron charges (2e), reflecting that the Cooper pair condensate must have an even parity. This ground state (GS) is foundational for all superconducting qubit devices. Here, we study a hybrid superconducting–semiconducting island and find three typical GS evolutions in a parallel magnetic field: a robust 2e-periodic even-parity GS, a transition to a 2e-periodic odd-parity GS, and a transition from a 2e- to a 1e-periodic GS. The 2e-periodic odd-parity GS persistent in gate-voltage occurs when a spin-resolved subgap state crosses zero energy. For our 1e-periodic GSs we explicitly show the origin being a single zero-energy state gapped from the continuum, i.e., compatible with an Andreev bound states stabilized at zero energy or the presence of Majorana zero modes.

Spin-momentum locking in a semiconductor device with strong spin-orbit coupling (SOC) is thought to be an important prerequisite for the formation of Majorana bound states 1-3 . Such a helical state is predicted in one-dimensional (1D) nanowires subject to strong Rashba SOC and spin-mixing 4 -its hallmark being a characteristic re-entrant behaviour in the conductance. Here, we report direct experimental observations of the re-entrant conductance feature, which reveals the formation of a helical liquid, in the lowest 1D subband of an InAs nanowire. Surprisingly, the feature is very prominent also in the absence of magnetic fields. This behaviour suggests that exchange interactions have a substantial impact on transport in our device. We attribute the opening of the pseudogap to spin-flipping two-particle backscattering 5-7 . The all-electric origin of the ideal helical transport could have important implications for topological quantum computing.A 1D conductor with strong SOC is predicted 1,2,8 to represent a viable host for Majorana bound states. These zero-energy states feature characteristic non-Abelian exchange statistics 8 and can be created by mimicking spinless p-wave Cooper pairing using a semiconductor nanowire with a helical state and inducing s-wave superconductivity. InAs and InSb nanowires are promising host materials to explore the existence and nature of Majorana bound states 9,10 . To this end, it is essential to both establish transport in 1D subbands and induce a helical state in the nanowire. The usual mechanism that is considered to open a helical gap involves an external Zeeman field oriented perpendicular to the uniaxial spinorbit field 4 . The magnitude of the spin-orbit energy relative to the Zeeman energy is partly responsible for the size of the topological energy gap that will protect the zero-energy Majorana modes 11 . However, Oreg et al. 2,12 and Stoudenmire et al. 13 have pointed out that such an energy gap can also result from strong electronic correlations. Several mechanisms have been proposed along these lines: for example, spin-flipping two-particle backscattering 7 and hyperfine interaction between nuclear spins and a Luttinger liquid 14 , both of which can open a gap. The latter mechanism has been invoked to explain a conductance reduction by a factor of two at low temperatures in a GaAs quantum wire 15 , but no re-entrant behaviour is predicted within this framework.Other than Quay et al. 3 , we report on a re-entrant conductance feature in the lowest subbands of InAs nanowire quantum point contacts (QPCs), which offer the desired strong SOC (see Supplementary Section 1). Moreover, our proposed spin-mixing mechanism does not necessarily rely on external time-reversal symmetry-breaking terms: while the effect is pronounced in the presence of an external magnetic field, it persists also in its absence. Guided by the observation 16 of the Landé g factor enhancement for the lowest subband 17 and by signatures of the 0.7 anomaly 18 , we identify the important role of exchange int...