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

TL;DR

This paper develops a hydrodynamic theory for transport near quantum critical points in 2D, predicting Nernst effect behavior and revealing connections to black hole physics via AdS/CFT correspondence.

Contribution

It introduces a universal hydrodynamic framework for quantum critical transport, linking condensed matter phenomena with holographic duality and providing exact results for a supersymmetric CFT.

Findings

Predicted Nernst signal dependence on magnetic field and temperature matching cuprate measurements.

Identified a hydrodynamic cyclotron mode observable in ultrapure samples.

Established agreement between hydrodynamic predictions and AdS/CFT exact results.

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.