Ward Identity and Homes' Law in a Holographic Superconductor with Momentum Relaxation

Abstract

We study three properties of a holographic superconductor related to conductivities, where momentum relaxation plays an important role. First, we find that there are constraints between electric, thermoelectric and thermal conductivities. The constraints are analytically derived by the Ward identities regarding diffeomorphism from field theory perspective. We confirm them by numerically computing all two-point functions from holographic perspective. Second, we investigate Homes' law and Uemura's law for various high-temperature and conventional superconductors. They are empirical and (material independent) universal relations between the superfluid density at zero temperature, the transition temperature, and the electric DC conductivity right above the transition temperature. In our model, it turns out that the Homes' law does not hold but the Uemura's law holds at small momentum relaxation related to coherent metal regime. Third, we explicitly show that the DC electric conductivity is finite for a neutral scalar instability while it is infinite for a complex scalar instability. This shows that the neutral scalar instability has nothing to do with superconductivity as expected.

31 pages, 14 figures, v2: minor changes, typos corrected, references added

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• Homes' law in holographic superconductor with linear-$T$ resistivity
• Linear-$T$ resistivity at high temperature
• Upper bound of the charge diffusion constant in holography
• Holographic Supersolids
• Holographic RG flow of thermo-electric transports with momentum dissipation
• Linear-$T$ resistivity from low to high temperature: axion-dilaton theories
• Universal scaling relations in electron-phonon superconductors
• Deep learning-based holography for T-linear resistivity
• Impurity-Driven Metal-Insulator Transitions in Holography