Thermo-electric transport in gauge/gravity models with momentum dissipation

Abstract

We present a systematic definition and analysis of the thermo-electric linear response in gauge/gravity systems focusing especially on models with massive gravity in the bulk and therefore momentum dissipation in the dual field theory. A precise treatment of finite counter-terms proves to be essential to yield a consistent physical picture whose hydrodynamic and beyond-hydrodynamics behaviors noticeably match with field theoretical expectations. The model furnishes a possible gauge/gravity description of the crossover from the quantum-critical to the disorder-dominated Fermi-liquid behaviors, as expected in graphene.

Figures (6)

• Figure 1: The static limit of the electric conductivity $\sigma_{DC}$ as a function of the scale invariant temperature $\tilde{T}$. The values of the parameter of the model are: $\mu=1, \; L=1$ and $\gamma=1$.
• Figure 2: Real (left) and imaginary (right) part of the thermal conductivity $\bar{\kappa}(\omega)$ for $\beta=-0.44$, $\gamma=0.6$ and $T/\mu=1$.
• Figure 3: Scattering rate $\tau^{-1}$ as a function of the scale invariant temperature $\tilde{T}$ for $\beta=-0.44$ , $\mu=1$, $\gamma=1$.
• Figure 4: Comparisons between the numerically computed (solid blue lines) thermo-electric conductivity $s_{DC}$ (left) and the numerically computed thermal conductivity $\bar{\kappa}_{DC}$ (right) with the hydrodynamic formulæ \ref{['sart']} and \ref{['kappaart']} (red dashed lines) for $\beta=-1.04, \; \mu=1, \; L=1, \;$ and $\gamma=0.6$.
• Figure 5: A magnification in the low $\tilde{T}$ region of the comparisons between the numerically computed (solid blue lines) thermo-electric conductivity $s_{DC}$ (left) and the numerically computed thermal conductivity $\bar{\kappa}_{DC}$ (right) with the hydrodynamic formulæ \ref{['sart']} and \ref{['kappaart']} (red dashed lines) for $\beta=-1.04, \; \mu=1, \; L=1, \;$ and $\gamma=0.6$.