A Dirty Holographic Superconductor

Abstract

We study the effects of disorder on a holographic superconductor by introducing a random chemical potential on the boundary. We consider various realizations of disorder and find that the critical temperature for superconductivity is enhanced. We also present evidence for a precise form of renormalization in this system. Namely, when the random chemical potential is characterized by a Fourier spectrum of the form $k^{-2α}$ we find that the spectra of the condensate and the charge density are again power-laws, whose exponents are accurately and universally governed by linear functions of $α$.

Figures (5)

• Figure 1: Average of the condensate as a function of the strength of disorder using $k_0=1$. The value of the condensate grows with increasing disorder strength, $w$.
• Figure 2: Phase diagram, dependence of the critical temperature on the strength of the noise.
• Figure 3: Initial chemical potential profile $\mu(x)=6.0+0.1 \sum\limits_{n=1}^{100} \frac{1}{2\pi n}\cos (2\pi n x +\delta_n)$ (left panel) and the corresponding condensate profile (right panel).
• Figure 4: Initial chemical potential profile $\mu(x)=6.0+0.1 \sum\limits_{n=1}^{100} \frac{1}{2\pi n}\cos (2\pi n x +\delta_n)$ (left panel) and the corresponding charge density profile (right panel).
• Figure 5: Renormalization of the disorder: Condensate $\Delta=1.9+1.0\,\alpha$ (left panel) and charge density $\Gamma= -0.88+ 1.0\,\alpha$ (right panel). This plot was made considering $k_0=2 \pi$, $\mu_0=6$ and $\epsilon=1$. We can see that the flater the spectrum, the larger the error. This might be associated with the fact that large momenta are more sensitive to the discretization.