Striped Superconductor and Holography

Using gauge/gravity duality, we analytically study the properties of a strongly coupled striped superconductor, with the charge density wave sourced by a modulated chemical potential. The calculation is done in the large modulation wavenumber $Q$ regime and comparing the results with numerical calculations, we find good agreement for $Q \geq 3 T_c$. 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 $\Delta < \frac{3}{2}$, whereas for $\Delta > \frac{3}{2}$, there is no phase transition above a certain critical value of $Q$. The order parameter or 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 also calculate the conductivity with its spatial dependence.