Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes (0706.3215v3)

Abstract: We present a general hydrodynamic theory of transport in the vicinity of superfluid-insulator transitions in two spatial dimensions described by "Lorentz"-invariant quantum critical points. We allow for a weak impurity scattering rate, a magnetic field B, and a deviation in the density, \rho, from that of the insulator. We show that the frequency-dependent thermal and electric linear response functions, including the Nernst coefficient, are fully determined by a single transport coefficient (a universal electrical conductivity), the impurity scattering rate, and a few thermodynamic state variables. With reasonable estimates for the parameters, our results predict a magnetic field and temperature dependence of the Nernst signal which resembles measurements in the cuprates, including the overall magnitude. Our theory predicts a "hydrodynamic cyclotron mode" which could be observable in ultrapure samples. We also present exact results for the zero frequency transport co-efficients of a supersymmetric conformal field theory (CFT), which is solvable by the AdS/CFT correspondence. This correspondence maps the \rho and B perturbations of the 2+1 dimensional CFT to electric and magnetic charges of a black hole in the 3+1 dimensional anti-de Sitter space. These exact results are found to be in full agreement with the general predictions of our hydrodynamic analysis in the appropriate limiting regime. The mapping of the hydrodynamic and AdS/CFT results under particle-vortex duality is also described.

• The paper develops a hydrodynamic theory demonstrating that universal conductivity and impurity scattering govern the Nernst effect near quantum critical points.
• The paper validates its predictions against experimental data on high-Tc superconductors and predicts a hydrodynamic cyclotron mode in ultrapure samples.
• The paper leverages AdS/CFT correspondence to connect condensed matter physics with high-energy theory, providing exact results for zero-frequency transport coefficients.

Overview of "Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes"

This paper presents a comprehensive paper of the Nernst effect in the context of quantum critical points (QCPs) in condensed matter systems, with applications extending to dyonic black holes via the AdS/CFT correspondence. The authors focus on superfluid-insulator transitions in two-dimensional systems characterized by Lorentz invariance at the QCPs and explore the implications of a weak impurity scattering rate, the presence of a magnetic field $B$, and deviations in the density $\rho$.

Key Contributions

• Hydrodynamic Theory Near QCPs: The authors develop a hydrodynamic framework to understand transport phenomena near superfluid-insulator transitions. They show that a single transport coefficient, the universal electrical conductivity $\sigma_Q$, along with the impurity scattering rate and thermodynamic variables, governs the system's response functions. These include the frequency-dependent thermal and electric linear response functions and the Nernst coefficient.
• Comparison with Experiments: Utilizing the developed theory, predictions for the temperature and magnetic field dependence of the Nernst signal are made, showing good agreement with experimental observations for high-Tc superconductors and NbSi films, aligning with qualitative and quantitative experimental data.
• Cyclotron Mode Prediction: A "hydrodynamic cyclotron mode" is predicted, which could be observable in ultrapure samples, suggesting a potential area for experimental exploration.
• AdS/CFT Correspondence: By using the AdS/CFT framework, the authors calculate exact results for zero-frequency transport coefficients in a supersymmetric CFT. These calculations involve mapping perturbations in the CFT to electric and magnetic charges in an anti-de Sitter space dyonic black hole setup, validating the hydrodynamic predictions in certain limits.

Theoretical and Practical Implications

1. Unified Description: The paper provides a unified hydrodynamic description applicable to various systems undergoing the superfluid-insulator transition at quantum criticality, highlighting the universal nature of the critical transport phenomena.
2. Extensions to High Magnetic Fields: The work opens avenues for exploring transport phenomena under high magnetic fields beyond the perturbative regime, potentially useful for practical applications in electronic devices that operate under extreme conditions.
3. Interplay with String Theory: The application of AdS/CFT highlights intriguing connections between condensed matter physics and high-energy theoretical physics, suggesting that insights from string theory could inform low-dimensional quantum systems' behavior.

Future Directions

Further research could explore:

• Detailed numerical simulations incorporating the hydrodynamic equations to provide refined predictions across broader regimes.
• Experimental investigations to detect and characterize the proposed cyclotron mode in systems akin to the cuprates under varying conditions.
• Extensions of the theory to include non-Lorentz-invariant QCPs and disordered systems, bridging the gap between idealized models and real-world materials.

This paper stands as a landmark contribution, providing a rigorous mathematical and conceptual framework for understanding complex transport phenomena near quantum phase transitions, with implications spanning both condensed matter physics and the quantum aspects of gravity.