Superroughening versus intrinsic anomalous scaling of surfaces

We study kinetically rough surfaces which display anomalous scaling in local properties such as the roughness or the height-difference correlation function. By studying the power spectrum of the surface and its relation to the height-difference correlation, we distinguish two independent causes for anomalous scaling. One is superroughening (global roughness exponent larger than or equal to 1), even if the spectrum behaves nonanomalously. Another cause is what we term an intrinsically anomalous spectrum, in whose scaling an independent exponent exists, which induces different scaling properties for small and large length scales. We show that in this case the surface does not need to be superrough in order to display anomalous scaling. The scaling relations we propose for the structure factor and height-difference correlation for intrinsically anomalous surfaces are shown to hold for a random diffusion equation, independently of the value of the global roughness exponent below or above one.