Strongly coupled striped superconductor with large modulation

Abstract

Using gauge/gravity duality, we analytically calculate properties of a strongly coupled striped superconductor, with the charge density wave sourced by a modulated chemical potential, in the large modulation wavenumber Q limit. In the absence of a homogeneous term in the chemical potential, we show that the critical temperature scales as a negative power of Q for scaling dimensions ∆ < 3 2 , whereas for ∆ > 3 2 , there is no phase transition above a certain critical value of Q. The condensate is found to scale as a positive power of Q such that the gap is proportional to Q.We discuss how these results change if a homogeneous term is added to the chemical potential.We compare our analytic results with numerical calculations whenever the latter are available and find good agreement.

Observing the inhomogeneity in the holographic models of superconductors

“…We see that as Q increases, the critical temperature becomes smaller. The influence of Q on the critical temperature is consistent with that observed in [10,12].…”

“…Some progresses have been made along this direction [10][11][12][13][14] in taking the holographic superconductor model one step closer to real systems by considering inhomogeneous configurations. Studying the inhomogeneous solutions of the holographic superconductor with a modulated chemical potential of wave vector Q, in the probe limit it was shown that below a critical temperature superconducting stripes develop and the critical temperature depends on the modulation's wave vector, which characterizes the inhomogeneity [10][11][12]. The effects of the inhomogeneity on the superconducting transition temperature by including the effects of backreaction onto the spacetime geometry was also examined in [13].…”

Intertwined orders in holography: pair and charge density waves

“…5 Holographic superconductors with spatially modulated orders have been studied in a number of setups, starting with [19], in which striped modulations were sourced by a periodic chemical potential, with many generalizations in the literature since then, e.g. [20][21][22][23][24]. A study of backreaction by adding a lattice in the form of a periodic potential was reported in [25].…”

Superconducting dome from holography

“…At the mean field level, it was shown in Ref. [8] that the δ = 1 and 3/2 < ∆ ≤ 3 case results in such a feature.…”