Model building in AdS/CMT: DC conductivity and Hall angle

Abstract

Using the bottom-up approach in a holographic setting, we attempt to study both the transport and thermodynamic properties of a generic system in $3+1$-dimensional bulk spacetime. We show the exact $1/T$ and ${T}^{2}$ dependence of the longitudinal conductivity and Hall angle, as seen experimentally in most copper-oxide systems, which are believed to be close to quantum critical point. This particular temperature dependence of the conductivities are possible in two different cases: (1) background solutions with scale invariant and broken rotational symmetry and (2) solutions with pseudoscaling and unbroken rotational symmetry, but only at low density limit. Generically, the study of the transport properties in a scale-invariant background solution, using the probe brane approach, at high density and at low temperature limit suggests we consider only metrics with two exponents. More precisely, the spatial part of the metric components should not be same, i.e. ${g}_{xx}\ensuremath{\ne}{g}_{yy}$. In doing so, we have generalized the above-mentioned behavior of conductivity with a very special behavior of specific heat which at low temperature goes as: ${C}_{V}\ensuremath{\sim}{T}^{3}$. However, if we break the scaling symmetry of the background solution by including a nontrivial dilaton, axion, or both and keep the rotational symmetry, then also we can generate such a behavior of conductivity, but only in the low density regime. As far as we are aware, this particular temperature dependence of both the conductivity and Hall angle is being shown for the first time using holography.