  We give analytical and numerical solutions for the zero modes of the Dirac
operator in topological SU(2) gauge backgrounds at nonzero chemical potential.
Continuation from imaginary to real chemical potential is used to
systematically derive analytical zero modes for calorons at arbitrary holonomy
and, in particular limits, for instantons and dyons (magnetic monopoles). For
the latter a spherical ansatz is explored as well. All the zero mode exhibit
stronger peaks at the core and negative regions in their densities. We discuss
the structure of the corresponding overlap matrix elements. For discretized
calorons on the lattice we consider the staggered operator and show that it
does possess (quartet quasi-)zero modes, whose eigenmodes agree very well with
the continuum profiles, also for nonzero chemical potential.
