Superfluid λ Transition in Charged AdS Black Holes

We observe a superfluid $\lambda$ transition in the $P-V$ criticality of charged AdS black holes, within a holographic extended thermodynamics that considers the variation of Newton's constant $G$. We calculate the critical exponents and find that they coincide with those of a superfluid transition in liquid $^4\text{He}$ and the Bose-Einstein condensation of hard-sphere Bose gas. Moreover, the independence of entropy and thermodynamic volume in the holographic framework allows us to construct a well-defined Ruppeiner metric. The associated scalar curvature suggests that the black holes show similar microscopic interactions with the hard-sphere Bose gas, where the superfluid (condensed) phase is dominated by repulsive interactions, while the normal (gas) phase is dominated by attractive interactions. These findings might provide us with new insights into the quantum aspect of charged AdS black holes.