INTRODUCTION

Majorana zero modes (MZMs) localized at the ends of one-dimensional topological superconductors are promising candidates for fault-tolerant quantum computing. One approach among the proposals to realize MZMsbased on semiconducting nanowires with strong spin-orbit coupling subject to a Zeeman field and superconducting proximity effecthas received considerable attention, yielding increasingly compelling experimental results over the past few years. An alternative route to MZMs aims to create vortices in topological superconductors, for instance, by coupling a vortex in a conventional superconductor to a topological insulator.

We intoduce a conceptually distinct approach to generating MZMs by threading magnetic flux through a superconducting shell fully surrounding a spin-orbitcoupled semiconducting nanowire core; this approach contains elements of both the proximitized-wire and vortex schemes. We show experimentally and theoretically that the winding of the superconducting phase around the shell induced by the applied flux gives rise to MZMs at the ends of the wire. The topological phase sets in at relatively low magnetic fields, is controlled by moving from zero to one phase twist around the superconducting shell, and does not require a large g factor in the semiconductor, which broadens the landscape of candidate materials.

In the destructive Little-Parks regime, the modulation of critical temperature with flux applied along the hybrid nanowire results in a sequence of lobes with reentrant superconductivity. Each lobe is associated with a quantized number of twists of the superconducting phase in the shell, determined by the external field. The result is a series of topologically locked boundary conditions for the proximity effect in the semiconducting core, with a dramatic effect on the subgap density of states.

Tunneling into the core in the zeroth superconducting lobe, around zero flux, we measure a hard proximity-induced gap with no subgap features. In the superconducting regions around one quantum of applied flux, 0 = h/2e, corresponding to phase twists of 2 in the shell, tunneling spectra into the core show stable zero-bias peaks, indicating a discrete subgap state fixed at zero energy.

Theoretically, we find that a Rashba field arising from the breaking of local radial inversion symmetry at the semiconductor-superconductor interface, along with 2-phase twists in the boundary condition, can induce a topological state supporting MZMs. We calculate the topological phase diagram of the system as a function of Rashba spin-orbit coupling, radius of the semiconducting core, and band bending at the superconductor-semiconductor interface. Our analysis shows that topological superconductivity extends in a reasonably large portion of the parameter space. Transport simulations of the tunneling conductance in the presence of MZMs qualitatively reproduce the experimental data in the entire voltage-bias range.

We obtain further experimental evidence that the zero-energy states are delocalized at wire ends by investigating Coulomb blockade conductance peaks in full-shell wire islands of various lengths. In the zeroth lobe, Coulomb blockade peaks show 2e spacing; in the first lobe, peak spacings are roughly 1e-periodic, with slight even-odd alternation that vanishes exponentially with island length, consistent with overlapping Majorana modes at the two ends of the Coulomb island. The exponential dependence on length, as well as incompatibility with a power-law dependence, provides compelling evidence that MZMs reside at the ends of the hybrid islands.

While being of similar simplicity and practical feasibility as the original nanowire proposals with a partial shell coverage, full-shell nanowires provide several key advantages. The modest magnetic field requirements, protection of the semiconducting core from surface defects, and locked phase winding in discrete lobes together suggest a relatively easy route to creating and controlling MZMs in hybrid materials. Our findings open the possibility of studying an interplay of mesoscopic and topological physics in this system.

(A) Colorized electron micrograph of a tunneling device composed of a hybrid nanowire with hexagonal semiconducting core and full superconducting shell. (B) Tunneling conductance (color) into the core as a function of applied flux (horizontal axis) and source-drain voltage (vertical axis) reveals a hard induced superconducting gap near zero applied flux and a gapped region with a discrete zero-energy state around one applied flux quantum, 0. (C) Realistic transport simulations in the presence of MZMs reproduce key features of the experimental data.

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Flux-induced topological superconductivity in full-shell nanowires - Science Magazine