DC resistivity of quantum critical, charge density wave states from gauge-gravity duality

TL;DR

Using holographic duality, the paper builds a homogeneous effective model for quantum critical CDWs and computes the dc resistivity from incoherent diffusion, independent of momentum relaxation. The authors derive an analytic expression for the incoherent conductivity and show how the low-temperature scaling is governed by IR data with exponents z and θ, allowing conducting or insulating ground states. They extend the analysis to unstable, semi-locally critical CDW phases, where uniform strain and marginal vs irrelevant deformations control the T-dependence, including possible Planckian, T-linear resistivity scenarios. The results offer a bridge between holographic transport and EFT descriptions of CDWs and relate to transport in underdoped cuprates, while noting the importance of thermodynamic stability in determining σ_o.

Abstract

In contrast to metals with weak disorder, the resistivity of weakly-pinned charge density waves (CDWs) is not controlled by irrelevant processes relaxing momentum. Instead, the leading contribution is governed by incoherent, diffusive processes which do not drag momentum and can be evaluated in the clean limit. We compute analytically the dc resistivity for a family of holographic charge density wave quantum critical phases and discuss its temperature scaling. Depending on the critical exponents, the ground state can be conducting or insulating. We connect our results to dc electrical transport in underdoped cuprate high $T_c$ superconductors. We conclude by speculating on the possible relevance of unstable, semi-locally critical CDW states to the strange metallic region.