Thermoelectric Conductivities at Finite Magnetic Field and the Nernst Effect

TL;DR

Problem: understanding thermoelectric transport and the Nernst effect in strongly coupled systems at finite magnetic field. Approach: holographic gauge/gravity duality applied to Einstein-Maxwell-dilaton theories with axion momentum relaxation; derive horizon-data formulas for DC conductivities $(oldsymbol{\sigma}, oldsymbol{\alpha}, oldsymbol{ar{oldsymbol{ar{oldsymbol{ar{oldsymbol{ar{ }}}}}}})$ and the Nernst signal $e_N = - {(oldsymbol{\sigma}^{-1}oldsymbol{\alpha})_y}^{x}$, and validate with numerical AC calculations on a dyonic black brane. Contributions: general analytic DC results expressed via horizon data, an explicit dyonic-axion model showing cuprate-like bell-shaped Nernst response for small momentum relaxation, and a full AC analysis that confirms DC limits and reveals cyclotron poles; analysis of Hall response and how momentum relaxation modulates transport. Significance: provides a controlled holographic framework to model magnetotransport in strongly correlated systems and offers insights relevant to cuprate phenomenology and quantum critical behavior.

Abstract

We study the thermoelectric conductivities of a strongly correlated system in the presence of a magnetic field by the gauge/gravity duality. We consider a class of Einstein-Maxwell-Dilaton theories with axion fields imposing momentum relaxation. General analytic formulas for the direct current(DC) conductivities and the Nernst signal are derived in terms of the black hole horizon data. For an explicit model study, we analyse in detail the dyonic black hole modified by momentum relaxation. In this model, for small momentum relaxation, the Nernst signal shows a bell-shaped dependence on the magnetic field, which is a feature of the normal phase of cuprates. We compute all alternating current(AC) electric, thermoelectric, and thermal conductivities by numerical analysis and confirm that their zero frequency limits precisely reproduce our analytic DC formulas, which is a non-trivial consistency check of our methods. We discuss the momentum relaxation effects on the conductivities including cyclotron resonance poles.

Figures (10)

• Figure 1: $\beta/T$ and $B/T$ dependence of DC conductivities at fixed $\mu/T =4$
• Figure 2: Hall angle $\theta_H = \arctan(\sigma^{xy}/\sigma^{xx})$
• Figure 3: Nernst signal
• Figure 4: Agreement of DC analytic formulas(solid curves) obtained in section \ref{['sec:DCconduct']} with numerical results(red dots): DC conductivities vs $\beta/T$ with $\mu/T=4$, $B/T^2 =1$
• Figure 5: $\beta$ dependence of electric conductivities: $\beta /T= 0, \ 0.5, \ 1, \ 1.5$(dotted, red, green, blue) with $\mu/T = 1, \ B/T^2=3$