The anomalous mix at the high-Z and low-Z plasma interfaces in an inertial confinement fusion hohlraum is a current topic of interest. The mechanism for such an anomalous mix in the interpenetration layer at the high-Z and low-Z plasma interface and its effects on the laser plasma instabilities have been investigated by particle-in-cell simulations. It is found that a diffusion-driven collisionless shock wave can be generated from an initially sharp high-Z and low-Z plasma interface with total pressure balance and constant temperature in the laser propagation channel. This purely electrostatic shock wave propagates into the high-Z plasma and leads to mix of different species of ions which is significantly faster than a classical mix in the presence of the large electric field. The mix layer width, measured as a separation distance affected by the shock, grows as , where . The effect of the anomalous mix on the linear growth rate of laser plasma instabilities is evaluated.