Coherent/incoherent metal transition in a holographic model

Abstract

Abstract: We study AC electric (σ), thermoelectric (α), and thermal (Formula presented.) conductivities in a holographic model, which is based on 3+1 dimensional Einstein-Maxwell-scalar action. There is momentum relaxation due to massless scalar fields linear to spatial coordinate. The model has three field theory parameters: temperature (T), chemical potential (μ), and effective impurity (β). At low frequencies, if β < μ, all three AC conductivities (σ, α,(Formula presented.)) exhibit a Drude peak modified by pair creation contribution (coherent metal). The parameters of this modified Drude peak are obtained analytically. In particular, if β ≪ μ the relaxation time of electric conductivity approaches to (Formula presented.) and the modified Drude peak becomes a standard Drude peak. If β > μ the shape of peak deviates from the Drude form (incoherent metal). At intermediate frequencies (T < ω < μ), we have analysed numerical data of three conductivities (σ, α,(Formula presented.)) for a wide variety of parameters, searching for scaling laws, which are expected from either experimental results on cuprates superconductors or some holographic models. In the model we study, we find no clear signs of scaling behaviour.