  Conventional $s$-wave superconductivity is understood to arise from singlet
pairing of electrons with opposite Fermi momenta, forming Cooper pairs whose
net momentum is zero [1]. Several recent studies have focused on structures
where such conventional $s$-wave superconductors are coupled to systems with an
unusual configuration of electronic spin and momentum at the Fermi surface.
Under these conditions, the nature of the paired state can be modified and the
system may even undergo a topological phase transition [2, 3]. Here we present
measurements and theoretical calculations of several HgTe quantum wells coupled
to either aluminum or niobium superconductors and subject to a magnetic field
in the plane of the quantum well. By studying the oscillatory response of
Josephson interference to the magnitude of the in-plane magnetic field, we find
that the induced pairing within the quantum well is spatially varying. Cooper
pairs acquire a tunable momentum that grows with magnetic field strength,
directly reflecting the response of the spin-dependent Fermi surfaces to the
in-plane magnetic field. In addition, in the regime of high electron density,
nodes in the induced superconductivity evolve with the electron density in
agreement with our model based on the Hamiltonian of Bernevig, Hughes, and
Zhang [4]. This agreement allows us to quantitatively extract the value of
$\tilde{g}/v_{F}$, where $\tilde{g}$ is the effective g-factor and $v_{F}$ is
the Fermi velocity. However, at low density our measurements do not agree with
our model in detail. Our new understanding of the interplay between spin
physics and superconductivity introduces a way to spatially engineer the order
parameter, as well as a general framework within which to investigate
electronic spin texture at the Fermi surface of materials.
