- The paper demonstrates that strange metals exhibit linear resistivity due to the minimal viscosity of their electronic fluid.
- It employs the memory matrix formalism and hydrodynamic models to connect electrical transport with momentum dissipation and entropy.
- The study paves the way for experimental and theoretical advances in understanding high-temperature superconductors and quantum critical behavior.
The paper, titled "Holographic duality and the resistivity of strange metals," tackles the enigmatic properties of strange metals, particularly their linear resistivity with temperature, by leveraging the framework of holographic duality. Authored by Richard A. Davison, Koenraad Schalm, and Jan Zaanen, it presents a theoretical investigation into the mechanisms driving the peculiar properties of these materials, exemplified by high-temperature superconductors like the cuprates.
Overview and Theoretical Insights
Strange metals, characterized by their unusual linear temperature dependence of resistivity, have long perplexed the physics community. Unlike Fermi liquids, their behavior suggests strong interactions and the absence of long-lived quasiparticles. The researchers employ holographic duality, a concept originating from string theory, to examine these properties. The duality posits a mathematical equivalence between strongly interacting quantum field theories and classical gravity models in higher-dimensional spaces.
The central thesis posits that the linear resistivity observed in strange metals arises from the minimal viscosity of the electronic fluid, which, unlike Fermi liquids, has significant implications for transport properties. Specifically, they present a mechanism where the resistivity is proportional to electronic entropy, a departure from traditional Fermi-liquid behavior, which could potentially account for the linear resistivity in cuprates.
Mechanism and Results
The mechanism detailed in the paper hinges on the notion of quenched disorder interacting with a strongly coupled, locally quantum critical state. This state is characterized by minimal viscosity, which becomes significant in determining the electrical transport properties. In this framework, the DC resistivity is tied to the momentum dissipation rate controlled by the system's thermodynamic entropy, which is linear with temperature in the strange metallic phase. This association is theoretically derived using the memory matrix formalism, providing a quantitative basis for their claims.
The authors introduce a hydrodynamic description to capture the transport in these strongly interacting systems, markedly differing from the quasiparticle-dominated transport in conventional metals. They draw parallels to examples of holographic duals exhibiting locally quantum critical IR fixed points and exploring the implications of their minimal viscosity, resulting in linear-in-temperature resistivity.
Implications and Future Directions
The implications of this work are profound for both theoretical and potential experimental exploration of high-temperature superconductors and strange metals. The holographic approach here not only yields insights into linear resistivity but also suggests a broader applicability to other phases of matter governed by similar strong correlations. The framework offers a potential resolution to the longstanding puzzle of strange metals and opens up new avenues for studying strongly correlated electron systems through the lens of holographic duality.
Additionally, the paper suggests further exploration into the hydrodynamic behavior of metallic states and the role of holography in uncovering universal transport properties. It encourages experimental validation through precision measurements of resistivity and entropy over varying temperatures and provides a foundation for a deeper understanding of quantum critical phenomena in condensed matter systems.
Conclusion
This paper contributes significantly to the theoretical landscape of strongly correlated electron systems by offering a holographic perspective on the resistivity of strange metals. It articulates a compelling mechanism that ties resistivity to entropy, supported by calculations within a dual gravitational framework, and lays the groundwork for reconciling theoretical predictions with experimental observations in high-temperature superconductors. As the field progresses, this work will undoubtedly serve as a cornerstone for subsequent research into the enigmatic behavior of strange metals and the broader implications of holographic duality in condensed matter physics.