Spatial behavior in a Mott insulator near the voltage-driven resistive transition

We develop a real space theory of the voltage bias driven transition from a Mott insulator to a correlated metal. Within our Keldysh mean field approach the problem reduces to a self-consistency scheme for the charge and spin profiles in this open system. We solve this problem for a two dimensional antiferromagnetic Mott insulator at zero temperature. The charge and spin magnitude is uniform over the system at zero bias, but a bias $V$ leads to spatial modulation over a lengthscale $\xi(V)$ near the edges. $\xi(V)$ grows rapidly and becomes comparable to system size as $V$ increases towards a threshold scale $V_c$. The linear response conductance of the insulator is zero with the current being exponentially small for $V \ll V_c$. The current increases rapidly as $V \rightarrow V_c$. Beyond $V_c$, we observe an inhomogeneous low moment antiferromagnetic metal, and at even larger bias a current saturated paramagnetic metal. We suggest an approximate scheme for the spectral features of this nonequilibrium system.