  The recent explosion of research interest in Weyl semimetals has led to many
proposed Weyl semimetal candidates and a few experimental observations of a
Weyl semimetal in real materials. Through this experience, we have come to
appreciate that typical Weyl semimetals host many Weyl points. For instance,
the first Weyl semimetal observed in experiment, TaAs, hosts 24 Weyl points.
Similarly, the Mo$_x$W$_{1-x}$Te$_2$ series, recently under study as the first
Type II Weyl semimetal, has eight Weyl points. However, it is well-understood
that for a Weyl semimetal without inversion symmetry but with time-reversal
symmetry, the minimum number of Weyl points is four. Realizing such a minimal
Weyl semimetal is fundamentally relevant because it would offer the simplest
"hydrogen atom" example of an inversion-breaking Weyl semimetal. At the same
time, transport experiments and device applications may be simpler in a system
with as few Weyl points as possible. Recently, TaIrTe$_4$ has been predicted to
be a minimal, inversion-breaking Weyl semimetal. However, crucially, the Weyl
points and Fermi arcs live entirely above the Fermi level, making them
inaccessible to conventional angle-resolved photoemission spectroscopy (ARPES).
Here we use pump-probe ARPES to directly access the band structure above the
Fermi level in TaIrTe$_4$. We directly observe Weyl points and topological
Fermi arcs, showing that TaIrTe$_4$ is a Weyl semimetal. We find that, in
total, TaIrTe$_4$ has four Weyl points, providing the first example of a
minimal inversion-breaking Weyl semimetal. Our results hold promise for
accessing exotic transport phenomena arising in Weyl semimetals in a real
material.
