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In this letter we discuss the influence of a U(1) chemical potential $\mu$ onthe existence of Gribov copies in a U(1) theory at finite temperature $T$. Weshow that the chemical potential conspires against the existence of Gribovcopies in the sense that it restricts the space of solutions of the consistencyequation for the gauge parameter. Explicit solutions are found for T=0, asfunction of $\mu$. In the finite temperature case we find also a class ofsolutions which satisfy the KMS boundary conditions in the euclidean timedirection, having also a vanishing behavior when $|\mathbf r|\to\infty$

Considerations about Gribov ambiguities for the abelian Higgs model in the presence of chemical potential and temperature