Abstract
We construct a holographic model describing the striped superconductor (SSC), which is characterized by the presence of pair density waves (PDW). We explicitly demonstrate that the SSC phase is implemented as the intertwined phase of charge density waves (CDW) order and uniform superconducting (SC) order. The interplay of PDW order, CDW order as well as the uniform SC order in SSC phase is studied. It is found that the PDW order is prominent when both CDW order and uniform SC order are balanced. The critical temperature of CDW becomes higher in the presence of the uniform SC order, but its charge density amplitude is suppressed. On the other hand, the SC order is not sensitive to the presence of CDW order. We also demonstrate that among all the possible solutions, the black hole in SSC phase has the lowest free energy and thus is thermodynamically favored.
Highlights
Dynamics is well described by the classical theory of gravity
In contrast to the previous holographic work in literature, we insist that the charge density waves (CDW) phase is implemented by breaking the translational invariance spontaneously and the SC phase is implemented by the standard U(1) symmetry breaking, rather than Stückelberg mechanism
We find that the critical temperature of CDW in the presence of SC is higher than that in the absence of SC, which is consistent with the phase diagram in figure 9
Summary
We consider a holographic model in four dimensional spacetime, in which gravity is coupled to a dilaton field, two U(1) gauge fields and a complex scalar field. Before this we argue that over a doubly charged black hole background, both translational symmetry and U(1) gauge symmetry could be spontaneously broken when the temperature drops down, giving rise to the CDW phase and SC phase, respectively. The coupling term ΦF G is absent in current paper, even in the limit x → 0, the striped black hole background will not go back to the solutions in [31], instead the charge density maintains the form as in eq (3.3) and goes to zero in the limit x → 0 To justify this we may plot the constant term of the charge density ρ(B0) as well as the CDW amplitude ρ(B2) as the function of temperature T and doping parameter x, as illustrated in figure 4 and figure 3. The charge density ρ(B0) and the saturated value η2(0) of the condensation grow up with x as well
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