Building a Holographic Superconductor

We show that a simple gravitational theory can provide a holographically dual description of a superconductor. There is a critical temperature, below which a charged condensate forms via a second order phase transition and the (dc) conductivity becomes infinite. The frequency dependent conductivity develops a gap determined by the condensate. We find evidence that the condensate consists of pairs of quasiparticles.

Figure 1

The condensate as a function of temperature for the two operators ${\mathcal{O}}_1$ and ${\mathcal{O}}_2$. The condensate goes to zero at $T=T_c\propto {\rho }^{1/2}$.

Figure 2

The formation of a gap in the real, dissipative, part of the conductivity as the temperature is lowered below the critical temperature. Results shown for both the ${\mathcal{O}}_1$ operator (left) and the ${\mathcal{O}}_2$ operator (right). There is also a delta function at $\omega =0$. The rightmost curve in each plot corresponds to $T/T_c=0.0066$ (left) and $T/T_c=0.0026$ (right).

Figure 3

The gap at small $T/T_c$, with frequency normalized by the condensate. The dashed curve on the left plot is (18).