  The electric-current stabilized semi-metallic state in the
quasi-two-dimensional Mott insulator Ca$_2$RuO$_4$ exhibits an exceptionally
strong diamagnetism. Through a comprehensive study using neutron and X-ray
diffraction, we show that this non-equilibrium phase assumes a crystal
structure distinct from those of equilibrium metallic phases realized in the
ruthenates by chemical doping, high pressure and epitaxial strain, which in
turn leads to a distinct electronic band structure. Dynamical mean field theory
calculations based on the crystallographically refined atomic coordinates and
realistic Coulomb repulsion parameters indicate a semi-metallic state with
partially gapped Fermi surface. Our neutron diffraction data show that the
non-equilibrium behavior is homogeneous, with antiferromagnetic long-range
order completely suppressed. These results provide a new basis for theoretical
work on the origin of the unusual non-equilibrium diamagnetism in
Ca$_2$RuO$_4$.
