  Materials that break time-reversal or inversion symmetry possess
nondegenerate electronic bands, which can touch at so-called Weyl points. The
spinor eigenstates in the vicinity of a Weyl point exhibit a well-defined
chirality $\pm 1$. Numerous works have studied the consequences of this
chirality, for example in unconventional magnetoelectric transport. However,
even a Weyl point with isotropic dispersion is not only characterized by its
chirality but also by the momentum dependence of the spinor eigenstates. For a
single Weyl point, this momentum-space spin structure can be brought into
standard "hedgehog" form by a unitary transformation, but for two or more Weyl
points, this is not possible. In this work, we show that the relative spin
structure of a pair of Weyl points has strong qualitative signatures in the
electromagnetic response. Specifically, we investigate the Friedel oscillations
in the induced charge density due to a test charge for a centrosymmetric system
consisting of two Weyl points with isotropic dispersion. The most pronounced
signature is that the amplitude of the Friedel oscillations falls off as
$1/r^4$ in directions in which both Weyl points exhibit the same spin
structure, while for directions with inverted spin structures, the amplitude of
the Friedel oscillations decreases as $1/r^3$.
