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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 condensated; ii) the ratio of the gap frequency in conductivity $ω_g$ to the critical temperature $T_c$ 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 $μ$ 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 $α$.