Spin-orbit-induced correlations of the local density of states in two-dimensional electron gas

We study the local density of states (LDOS) of two-dimensional electrons in the presence of spin-orbit (SO) coupling. Although SO coupling has no effect on the average density of states, it manifests itself in the correlations of the LDOS. Namely, the correlation function acquires two satellites centered at energy difference equal to the SO splitting, $2\omega_{SO}$, of the electron Fermi surface. For a smooth disorder the satellites are well separated from the main peak. Weak Zeeman splitting $\omega_{Z} \ll \omega_{SO}$ in a parallel magnetic field causes an anomaly in the shape of the satellites. We consider the effect of SO-induced satellites in the LDOS correlations on the shape of the correlation function of resonant-tunneling conductances at different source-drain biases, which can be measured experimentally. This shape is strongly sensitive to the relation between $\omega_{SO}$ and $\omega_{Z}$.