Tunneling between 2D electron layers with correlated disorder: anomalous sensitivity to spin-orbit coupling

Tunneling between two-dimensional electron layers with mutually correlated disorder potentials is studied theoretically. Due to this correlation, the diffusive eigenstates in different layers are almost orthogonal to each other. As a result, a peak in the tunnel $I$-$V$ characteristics shifts towards small bias, $V$. If the correlation in disorder potentials is complete, the peak position and width are governed by the spin-orbit coupling in the layers; this coupling lifts the orthogonality of the eigenstates. Possibility to use inter-layer tunneling for experimental determination of weak {\em intrinsic} spin-orbit splitting of the Fermi surface is discussed.