Surface waves on the relativistic quantum plasma half-space

•We investigate the dispersion relations of surface waves in the relativistic quantum frame.•The frequency of SPPs has a blue-shift due to quantum effects.•Surface Langmuir oscillations can propagate on the cold plasma half-space due to quantum effects.•Relativistic quantum effects to SPPs and electrostatic surface waves are significant and observable.

We present a theoretical investigation on the propagation of surface waves on the relativistic quantum plasma half-space. The dispersion relations of surface plasmon polaritons (SPPs) and electrostatic surface waves containing relativistic quantum corrected terms are derived. Results show that the frequency of SPPs has a blue-shift, and surface Langmuir oscillations can propagate on the cold plasma half-space due to quantum effects. Numerical evaluation indicates that quantum effects to SPPs and electrostatic surface waves are significant and observable.