incoherent metal transition in a holographic model

We study AC electric (sigma), thermoelectric (alpha), and thermal ((kappa) over bar) 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 (mu), and effective impurity (beta). At low frequencies, if beta < mu, all three AC conductivities (sigma, alpha, <(kappa)over bar>) exhibit a Drude peak modified by pair creation contribution (coherent metal). The parameters of this modified Drude peak are obtained analytically. In particular, if beta << mu the relaxation time of electric conductivity approaches to 2 root 3 mu/beta(2) and the modified Drude peak becomes a standard Drude peak. If beta > mu the shape of peak deviates from the Drude form (incoherent metal). At intermediate frequencies (T < omega < mu), we have analysed numerical data of three conductivities (sigma, alpha, (kappa) over bar) 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.We would like to thank Yunkyu Bang, Richard Davison, Aristomenis Donos, Jerome Gauntlett, Xian-Hui Ge, Blaise Gouteraux, Takaaki Ishii, Yan Liu, Ya-Wen Sun, and Marika Taylor for valuable discussions and correspondence. The work of KYK and KKK was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science, ICT & Future Planning (NRF-2014R1A1A1003220). The work of SS and YS was supported by Mid-career Researcher Program through the National Research Foundation of Korea (NRF) grant No. NRF-2013R1A2A2A05004846. YS was also supported in part by Basic Science Research Program through NRF grant No. NRF-2012R1A1A2040881. We acknowledge the hospitality at APCTP ("Aspects of Holography", Jul. 2014) and Orthodox Academy of Crete ("Quantum field theory, string theory and condensed matter physics", Sep. 2014), and at CERN ("Numerical holography", Dec. 2014), where part of this work was done