A Maxwell-vector p-wave holographic superconductor in a particular background AdS black hole metric

We study the p-wave holographic superconductor for AdS black holes with planar event horizon topology for a particular Lovelock gravity, in which the action is characterized by a self-interacting scalar field nonminimally coupled to the gravity theory which is labeled by an integer $k$. As the Lovelock theory of gravity is the most general metric theory of gravity based on the fundamental assumptions of general relativity, it is a desirable theory to describe the higher dimensional spacetime geometry. The present work is devoted to studying the properties of the p-wave holographic superconductor by including a Maxwell field which nonminimally couples to a complex vector field in a higher dimensional background metric. In the probe limit, we find that the critical temperature decreases with the increase of the index $k$ of the background black hole metric, which shows that a larger $k$ makes it harder for the condensation to form. We also observe that the index $k$ affects the conductivity and the gap frequency of the holographic superconductors.