Determination of Dynamical exponents of Graphene at quantum critical point by holography

Abstract

We calculate the transport of a theory with two conserved currents by holographic method and compare it with graphene data to determine its dynamical exponents $(z,\theta)$ which characterizes a QCP. As a result, we find that the electric and the thermal conductivity data can be fit much more naturally if we assume $(z,\theta)=(3/2,1)$ rather than $(1,0)$. Furthermore, we find that thermoelectric power data at high temperature can be fit if we use $(3/2,1)$ but not at all by $(1,0)$. The $\theta=1$ result can be interpreted as taking into account the fermionic nature of the electrons and $z=3/2$ can be interpreted as the flattened band by the strong interaction.