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.
Highlights
To construct black holes dual to helical lattices [24,25,26,27]
We numerically compute alternating current (AC) electric (σ), thermoelectric (α, α), and thermal (κ) conductivity and confirm their zero frequency limits agree to the direct current (DC) formulas that we have derived analytically
Some examples of the AC electric conductivity are shown in figure 5 and 8; the thermoelectric conductivity is in figure 6; and the thermal conductivity is in figure 7
Summary
We will derive analytic formulas for the DC conductivities (σ, α, α, κ) in the presence of a magnetic field, from a general class of Einstein-Maxwell-Dilaton theories with axion fields (χ1, χ2). The background becomes the AdS-dynonic black hole geometry with the momentum relaxation. After using the Einstein equations for fluctuations with the ansatz (2.17)–(2.18), 2U (r)δgtx(r) = 2B2Z(φ)e−2v(r) + 2β2Φ(φ)e−v(r) + U (r) v 2(r) − φ 2(r) δgtx(r). Which, in turn, give us two algebraic equations for δgt(ih) of which solutions are δgt(ih). The conductivities are obtained by differentiating the boundary currents (Ji(∞), Qi(∞)) with respect to the external electric field (Ei) or the thermal. B T Σ1 ij , κij κ ̄ij ij , which are expressed in terms of the black hole horizon data
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