Holographic superconductivity from higher derivative theory

We construct a 6 derivative holographic superconductor model in the 4-dimensional bulk spacetimes, in which the normal state describes a quantum critical (QC) phase. The phase diagram (γ1,Tˆc) and the condensation as the function of temperature are worked out numerically. We observe that with the decrease of the coupling parameter γ1, the critical temperature Tˆc decreases and the formation of charged scalar hair becomes harder. We also calculate the optical conductivity. An appealing characteristic is a wider extension of the superconducting energy gap, comparing with that of 4 derivative theory. It is expected that this phenomena can be observed in the real materials of high temperature superconductor. Also the Homes' law in our present models with 4 and 6 derivative corrections is explored. We find that in certain range of parameters γ and γ1, the experimentally measured value of the universal constant C in Homes' law can be obtained.