Enhancement of critical temperature of a striped holographic superconductor

Abstract

We study the interplay between the stripe order and the superconducting order in a strongly coupled striped superconductor using gauge/gravity duality. In particular, we study the effects of inhomogeneity introduced by the stripe order on the superconducting transition temperature beyond the mean field level by including the effects of backreaction onto the spacetime geometry in the dual gravitational picture. We find that inhomogeneity enhances the critical temperature relative to its value for the uniform system.

Superconducting dome from holography

“…Another hint we obtained from our previous work is that in the δ = 1, and the δ = 1, 1/2 < ∆ ≤ 3/2 cases, fluctuations cause a significant drop in the critical temperature at small Q [7]. Combining the above, we expect that when the chemical potential averages to zero (δ = 1) and the scaling dimension of the order parameter satisfies 3/2 < ∆ ≤ 3, the superconducting regime is capped at larger values of Q, while when the fluctuations are turned on, it is capped at the smaller values of Q, thus resulting in a superconducting dome.…”

“…In the normal state, where the order parameter vanishes, and therefore φ = 0, the solution for the metric for arbitrary δ is given in [7]. Up to O(1/q 2 ), the solution for δ = 1 is then given by…”

“…In order to achieve the goal set in the previous section, following [7], we consider an Einstein-Maxwell-scalar system on a 3+1-dimensional spacetime with a negative cosmological constant Λ = −3/L 2 as a holographic model of a 2 + 1-dimensional strongly coupled striped superconductor. The bulk scalar field is dual to the superconducting order parameter, while the bulk U (1) gauge field is dual to the four-current in the strongly coupled system.…”

A simple holographic model of a charged lattice

“…These systems are commonly denoted as "holographic lattices". Prior to this development, there have been studies of perturbative lattice solutions on top of a metallic phase [6][7][8][9][10], and in the context of striped superconductors [11][12][13][14].…”

Observing the inhomogeneity in the holographic models of superconductors

“…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].…”