[Paper Review] DC resistivity at holographic charge density wave quantum critical points

Andrea Amoretti, Daniel Areán+2 more|arXiv (Cornell University)|Dec 21, 2017

Physics of Superconductivity and Magnetism3 citations

TL;DR

This paper analytically computes the dc resistivity in holographic charge density wave quantum critical points using a clean-limit approach, revealing that incoherent diffusive processes dominate transport. It finds that the resistivity exhibits distinct temperature scaling depending on critical exponents, with a finite residual resistivity at zero temperature in locally critical cases, offering insights into underdoped cuprates.

ABSTRACT

In contrast to metals with weak disorder, the resistivity of weakly-pinned charge density waves (CDW) 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 points and discuss its temperature scaling. Depending on the critical exponents, the ground state can be conducting or insulating. In the locally critical case, it exhibits a residual resistivity at zero temperature. We discuss the relevance of our results to dc electrical transport in underdoped cuprate high $T_c$ superconductors.

Motivation & Objective

• To understand the nature of dc electrical resistivity in charge density wave quantum critical points beyond weak disorder models.
• To investigate how incoherent, momentum-non-conserving processes govern resistivity in clean systems.
• To determine the temperature scaling of resistivity in holographic models with varying critical exponents.
• To explore whether the ground state is conducting or insulating based on critical behavior.
• To connect the findings to the transport properties of underdoped cuprate high-Tc superconductors.

Proposed method

• Uses holographic duality (AdS/CFT) to model charge density wave quantum critical points in strongly correlated systems.
• Analyzes the clean limit where momentum relaxation is not driven by disorder, focusing on incoherent diffusive transport.
• Computes the dc resistivity via the Kubo formula applied to the boundary field theory dual to the bulk gravitational system.
• Considers a family of models with varying critical exponents to study their impact on resistivity scaling.
• Evaluates the zero-temperature limit to determine the existence of residual resistivity in locally critical cases.
• Relies on the gravity dual of the quantum critical point to extract transport coefficients without phenomenological assumptions.

Experimental results

Research questions

• RQ1 How does dc resistivity scale with temperature in holographic charge density wave quantum critical points?
• RQ2 What is the role of incoherent diffusive processes in determining resistivity when momentum relaxation is not disorder-driven?
• RQ3 Under what conditions does the ground state exhibit a finite residual resistivity at zero temperature?
• RQ4 How do critical exponents influence whether the ground state is conducting or insulating?
• RQ5 To what extent can these holographic results explain the resistivity behavior in underdoped cuprates?

Key findings

• The dc resistivity is dominated by incoherent, diffusive processes that do not carry momentum, valid in the clean limit.
• Resistivity scaling depends critically on the critical exponents, with distinct behaviors in the locally critical case.
• In the locally critical case, a finite residual resistivity persists at zero temperature, indicating a non-Fermi liquid ground state.
• The ground state can be either conducting or insulating depending on the value of the critical exponents.
• The model provides a framework consistent with the non-Fermi liquid resistivity observed in underdoped cuprate superconductors.