Holographic superconductor/insulator transition with logarithmic electromagnetic field in Gauss-Bonnet gravity

The behaviors of the holographic superconductors/insulator transition are studied by introducing a charged scalar field coupled with a logarithmic electromagnetic field in both the Einstein-Gauss-Bonnet AdS black hole and soliton. For the Einstein-Gauss-Bonnet AdS black hole, we find that: i) the larger coupling parameter of logarithmic electrodynamic field b makes it easier for the scalar hair to be condensed; ii) the ratio of the gap frequency in conductivity ωg to the critical temperature Tc depends on both b and the Gauss-Bonnet constant α; and iii) the critical exponents are independent of the b and α. For the Einstein-Gauss-Bonnet AdS soliton, we show that the system is the insulator phase when the chemical potential μ is small, but there is a phase transition and the AdS soliton reaches the superconductor (or superfluid) phase when μ is larger than critical chemical potential. A special property should be noted is that the critical chemical potential is not changed by the coupling parameter b but depends on α.