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

Sean A. Hartnoll, Pavel K. Kovtun, Markus Müller, and Subir Sachdev
Phys. Rev. B 76, 144502 – Published 4 October 2007

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 ρ 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 coefficients of a supersymmetric conformal field theory (CFT), which is solvable by the anti–de Sitter (AdS)/CFT correspondence. This correspondence maps the ρ 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.

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  • Received 3 July 2007

DOI:https://doi.org/10.1103/PhysRevB.76.144502

©2007 American Physical Society

Authors & Affiliations

Sean A. Hartnoll1, Pavel K. Kovtun1, Markus Müller2, and Subir Sachdev2

  • 1Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106-4030, USA
  • 2Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA

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Vol. 76, Iss. 14 — 1 October 2007

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