The general double cover of P^3 branched along a surface of degree 4, 6, or 8 carries a stable rank 2 Ulrich bundle, with moduli components of dimension 5, 6, and 0.
Elliptic curves, ACM bundles and Ulrich bundles on prime Fano threefolds
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Ulrich bundles on double coverings of projective space
The general double cover of P^3 branched along a surface of degree 4, 6, or 8 carries a stable rank 2 Ulrich bundle, with moduli components of dimension 5, 6, and 0.