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Hybrid superconductor-semiconductor materials are fueling research in
mesoscopic physics and quantum technology. Recently demonstrated smooth
$\beta$-Sn superconductor shells, due to the increased induced gap, are
expanding the available parameter space to new regimes. Fabricated on
quasiballistic InSb nanowires, with careful control over the hybrid interface,
Sn shells yield critical current-normal resistance products exceeding
temperature by at least an order of magnitude even when nanowire resistance is
of order 10k$\Omega$. In this regime Cooper pairs travel through a purely 1D
quantum wire for at least part of their trajectory. Here, we focus on the
evolution of supercurrent in magnetic field parallel to the nanowire. Long
decay up to fields of 1T is observed. At the same time, the decay for higher
occupied subbands is notably faster in some devices but not in others. We
analyze this using a tight-binding numerical model that includes the Zeeman,
orbital and spin-orbit effects. When the first subband is spin polarized, we
observe a dramatic suppression of supercurrent, which is also confirmed by the
model and suggests an absence of significant triplet supercurrent generation.
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