Ulrich line bundles on double planes

Consider a smooth complex surface \(X\) which is a double cover of the projective plane \(\mathbb{P}^2\) branched along a smooth curve of degree \(2s\). In this article, we study the geometric conditions which are equivalent to the existence of Ulrich line bundles on \(X\) with respect to this double covering. Also, for every \(s\geq 1\), we describe the classes of such surfaces which admit Ulrich line bundles and give examples.