Heun’s equation and analytic structure of the gap in holographic superconductivity

Abstract

Abstract We present the new method to calculate the critical temperature as a function of $$\Delta $$ Δ , conformal dimension of the cooper operator. We find that, in the regime $$1/2\le \Delta <1$$ 1 / 2 ≤ Δ < 1 where the AC conductivity does not show a gap, the critical temperature is not well defined. We also got expression of AC conductivity for $$\Delta =2$$ Δ = 2 , which agrees with numerical result in the probe approximation.