Abstract
The protection against backscattering provided by topology is a striking property. In two-dimensional insulators, a consequence of this topological protection is the ballistic nature of the one-dimensional helical edge states. One demonstration of ballisticity is the quantized Hall conductance. Here we provide another demonstration of ballistic transport, in the way the edge states carry a supercurrent. The system we have investigated is a micrometre-long monocrystalline bismuth nanowire with topological surfaces, that we connect to two superconducting electrodes. We have measured the relation between the Josephson current flowing through the nanowire and the superconducting phase difference at its ends, the current–phase relation. The sharp sawtooth-shaped phase-modulated current–phase relation we find demonstrates that transport occurs selectively along two ballistic edges of the nanowire. In addition, we show that a magnetic field induces 0–π transitions and ϕ0-junction behaviour, providing a way to manipulate the phase of the supercurrent-carrying edge states and generate spin supercurrents.
Highlights
The protection against backscattering provided by topology is a striking property
The sharp sawtooth-shaped current–phase relation (CPR) we find demonstrates that transport of Cooper pairs occurs ballistically[9,10,11,12,13] along two edges of the nanowire, whose positions can be deduced from experiments in different magnetic field orientations
The CPR of a Bi-nanowire-based Josephson junction demonstrates that conduction occurs along ballistic channels confined at two edges of the wire’s (111) facets
Summary
The protection against backscattering provided by topology is a striking property. In two-dimensional insulators, a consequence of this topological protection is the ballistic nature of the one-dimensional helical edge states. Notable exceptions occur when topology provides protection against disorder, such as in the quantum Hall effect or the recently discovered quantum spin Hall effect in two-dimensional (2D) topological insulators[1,2] In the latter, crystalline symmetry combined with high spin–orbit coupling generate band inversion and one-dimensional (1D) chiral edge states with perfect spin-momentum locking, that theoretically precludes backscattering along the edges. We provide a direct signature of ballistic 1D transport along the topological surfaces of a monocrystalline bismuth nanowire connected to superconducting electrodes To this end, we measure the relation between the Josephson current IJ flowing through a nanostructure and the superconducting phase difference j at its ends, the current–phase relation (CPR)[8]. We show that a Zeeman field induces 0–p transitions[14] and j0-junction behaviour[15], in agreement with recent theoretical predictions[16]
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