  Depending on the geometry of their Fermi surfaces, Weyl semimetals and their
analogues in classical systems have been classified into two types. In type I
Weyl semimetals (WSMs), the cone-like spectrum at the Weyl point (WP) is not
tilted, leading to a point-like closed Fermi surface. In type II WSMs, on the
contrary, the energy spectrum around the WP is strongly tilted such that the
Fermi surface transforms from a point into an open surface. Here, we
demonstrate, both theoretically and experimentally, a new type of (classical)
Weyl semimetal whose Fermi surface is neither a point nor a surface, but a flat
line. The distinctive Fermi surfaces of such semimetals, dubbed as type III or
zero-index WSMs, gives rise to unique physical properties: one of the edge
modes of the semimetal exhibits a zero index of refraction along a specific
direction, in stark contrast to types I and II WSMs for which the index of
refraction is always non-zero. We show that the zero-index response of such
topological phases enables exciting applications such as extraordinary wave
transmission (EOT).
