  We investigate energy resolved electric current from various correlated host
materials under out-of-equilibrium conditions. We find that, due to a combined
effect of electron-electron interactions, non-equilibrium and multi-particle
tunnelling, the energy resolved current is finite even above the Fermi edge of
the host material. In most cases, the current density possesses a singularity
at the Fermi level revealing novel manifestations of correlation effects in
electron tunnelling. By means of the Keldysh non-equilibrium technique, the
current density is calculated for one-dimensional interacting electron systems
and for two-dimensional systems, both in the pure limit and in the presence of
disorder. We then specialise to the field emission and provide a comprehensive
theoretical study of this effect in carbon nanotubes.
