A current corresponds to transfer of energy, but if you are not supplying any energy (via an applied bias) you cannot have a current flow. What happens at 0 V is that a dipole layer is formed in the middle which balances the difference in chemical potential out. The formation of this dipole layer is equivalent to a local current, in a transient sense, but the net final current will be zero. This is also clear from the formula, where you (in the zero-temperature limit) integrate from Ef-V/2 (Ef is the common Fermi level) to Ef+V/2 where V is the bias. If V=0 the integration interval is zero so the integral must be zero.
If you apply a different electron temperature to both sizes, you can get a current at zero bias, but then you are injecting energy into the system by keeping the reservoirs (the electrodes) at constant different temperatures.
