  It is known that contrary to expectations, the order parameter of chiral
symmetry breaking, the Dirac spectral density at zero virtuality does not
vanish above the critical temperature of QCD. Instead, the spectral density
develops a pronounced peak at zero. We show that the spectral density in the
peak has large violations of the expected volume scaling. This anomalous
scaling and the statistics of these eigenmodes is consistent with them being
produced by mixing instanton and antiinstanton zero modes. Consequently, we
show that a nonvanishing topological usceptibility implies a finite density of
eigenvalues around zero, which can have implications on the restoration of
chiral symmetry above the critical temperature.
