  Topological insulators are described by topological invariants that can be
computed by integrals over momentum space, but also as traces over local,
real-space topological markers. These markers are useful to detect topological
insulating phases in disordered crystals, quasicrystals and amorphous systems.
Among these markers, only the spectral localizer operator can be used to
distinguish topological metals, that show zero-modes of the localizer spectrum.
However, it remains unclear whether trivial metals also display zero-modes, and
if their localizer spectrum is distinguishable from topological ones. Here, we
show that trivial metals generically display zero-modes of the localizer
spectrum. The localizer zero-modes are determined by the zero-mode solutions of
a Dirac equation with a varying mass parameter. We use this observation, valid
in any dimension, to determine the difference between the localizer spectrum of
trivial and topological metals, and conjecture the spectrum of the localizer
for fractional quantum Hall edges. Because the localizer is a local, real-space
operator, it may be used as a tool to differentiate between non-crystalline
topological and trivial metals, and characterize strongly correlated systems,
for which local topological markers are scarce.
