PIRSA:07100036

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

Müller, M. (2007). Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes. Perimeter Institute. https://pirsa.org/07100036

Müller, Markus. Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes. Perimeter Institute, Oct. 23, 2007, https://pirsa.org/07100036 

          @misc{ pirsa_PIRSA:07100036,
            doi = {10.48660/07100036},
            url = {https://pirsa.org/07100036},
            author = {M{\"u}ller, Markus},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Theory of the Nernst effect near quantum phase transitions in condensed matter, and in dyonic black holes},
            publisher = {Perimeter Institute},
            year = {2007},
            month = {oct},
            note = {PIRSA:07100036 see, \url{https://pirsa.org}}
          }

Markus Müller

Institute for Quantum Optics and Quantum Information (IQOQI) - Vienna

Talk number
PIRSA:07100036
Collection
Talk Type
Subject
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.