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

By S. Hartnoll, P. Kovtun, Markus P. Mueller, S. Sachdev. 2007

622 citations recorded by the source corpus.

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 $\ensuremath{\rho}$ 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 coefficients of a supersymmetric conformal field theory (CFT), which is solvable by the anti\char21{}de Sitter (AdS)/CFT correspondence. This correspondence maps the $\ensuremath{\rho}$ and $B$ perturbations of the $2+1$ dimensional CFT to electric and magnetic charges of a black hole in the $3+1$ dimensional anti\char21{}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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/f4b7594852ee9f81728ec3bf5350fdbd768cc017

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Condensed Matter Physics

In Nuclear and High Energy Physics

Citations in the corpus

Black hole chemistry: thermodynamics with Lambda (2016, background): “The introduction of a negative cosmological constant implied that black holes could exhibit phase behaviour [13], and somewhat later led to the holographic deployment of black holes as systems dual to those in conformal field theories [14–16], quantum chromodynamics [17], and condensed matter physic”
Heating up Galilean holography (2008, background): “Fermions at unitarity are conjectured to realize this Schrödinger symmetry.”
The gravity dual of a p-wave superconductor (2008, background): “( −m(2)eff)ψ = 0 , (2) (3)It has been suggested [12, 13] that RNAdS black holes are dual to a close analog of the pseudogap state of high Tc materials.”
Landscape of superconducting membranes (2009, background): “However, one might certainly wish to consider dyonic black holes also (for instance to study phenomena such as the Hall or Nernst effects [46, 47, 49]) for which this term does not vanish.”
Momentum dissipation and effective theories of coherent and incoherent transport (2014, methodology): “We can determine the heat conductivity κ(ω, k) from the longitudinal Greens functions using the Kubo formula [2]”
Universal Resistivity from Holographic Massive Gravity (2013, background): “14) is in agreement with that proposed in [30].”
Building an AdS/CFT superconductor (2008, background): “Phenomena such as the Hall effect [3] and Nernst effect [4, 5, 6] have dual gravitational descriptions.”
Holography of dyonic dilaton black branes (2010, methodology): “From general reasoning based on linear response in magnetohydrodynamics it was argued in [13] (see also [14]) that at small frequency”
Breaking an Abelian gauge symmetry near a black hole horizon (2008, neutral): “ar X January 2008”
A note on generalized hydrodynamics: inhomogeneous fields and other concepts (2016, background): “Accordingly the hydrodynamic conservation equations become [42] (keeping the (x , t)-dependence implicit), at the first order in a derivative expansion, ∂ν〈T〉= F〈Jν〉, ∂μ〈J〉= 0 (38) where T is the energy-momentum tensor, F01 = −F10 = ∂x V0 and F00 = F11 = 0, and averages are taken in local fluid cell”
Peculiar properties of a charged dilatonic black hole in AdS 5 (2009, background): “The AdS4-Reissner-Nordstrom black hole was one of the first gravity models to be considered in this context [2, 3, 4].”
Parity-violating hydrodynamics in 2 + 1 dimensions (2011, background): “17) with hB = 0 is the canonical expression for the stress tensor and current of a fluid at non-zero B and Ω = 0, see for example [4, 61].”
Ohm's law at strong coupling: S duality and the cyclotron resonance (2007, background): “In fact, we will recover precisely the expressions derived from magnetohydrodynamics in [16].”
Fracton hydrodynamics (2020, background): “[81] Sean A.”
Lectures on holographic methods for condensed matter physics (2009, methodology): “The effect of the last term in this equation upon the hydrodynamic expressions for the conductivity (151) and (152) is to let ω → ω+ i/τimp [79].”