  In this work, we theoretically study the quantum correlations present in an
optomechanical system by invoking an additional cross-Kerr coupling between the
optical and mechanical mode. Under experimentally achievable conditions, we
first show that a significant enhancement of the steady-state entanglement
could be achieved at a considerably lower driving power, which is also
extremely robust with respect to system parameters and environmental
temperature. Then, we employ Gaussian quantum discord as a witness of the
genuine quantumness of the correlation present in the system and discuss its
dependence on the cross-Kerr nonlinearity.
