A Holographic Model for Pseudogap in BCS-BEC Crossover (I): Pairing Fluctuations, Double-Trace Deformation and Dynamics of Bulk Bosonic Fluid

摘要

We build a holographic model for the pairing fluctuation pseudogap phase infermionic high temperature superconductivity/superfluidity based on the BCS-BECcrossover scenario. The pseudogap originates from incoherent Cooper pairing andhas been observed in recent cold atom experiments. The strength of Cooperpairing and hence the BCS-BEC crossover is controlled by an effective 4-Fermiinteraction and we argue that the double-trace deformation for charged scalaroperator is a close analog in large N field theories. We employ thedouble-trace deformed Abelian Higgs model of holographic superconductors andpropose that the incoherent fluctuations of the charged scalar in the bulk isthe holographic dual of the fluctuating Cooper pairs. Using a Madelungtransformation and the velocity-potential formalism, we develop a quantum fluiddynamics as an effective theory for these bulk fluctuations. The new fluiddynamics takes care of the boundary conditions required by AdS/CFT and encodesthe vacuum polarization effect in curved spacetime. The pseudogap inconductivity can be related to the plasma oscillation of this bulk fluid.