Magneto-thermal transport implies an incoherent Hall conductivity

Abstract

We consider magnetohydrodynamics with an external magnetic field. We find that in general one must allow for a non-zero incoherent Hall conductivity to correctly describe the DC longitudinal and Hall thermal conductivities beyond order zero in the magnetic field expansion. We apply our result to the dyonic black hole, determining the incoherent Hall conductivity in that case, and additionally prove that the existence of this transport coefficient leads to a significantly better match between the hydrodynamic and AC thermo-electric correlators.

Collective modes of polarizable holographic media in magnetic fields

“…which are equivalent to the familiar conditions of the dielectric function, e.g (ω, k) = 0 for longitudinal excitations [37], and allow for dynamical electromagnetic interactions in the dual field theory without a driving external current, as needed for obtaining collective modes. This is a crucial difference with respect to the previous studies considering the same Reissner-Nordström dyonic black hole solution [38,39]. In the limit λ = 0, the b.c.s.…”

“…An obvious extension of our work is to introduce a charge density background Q = 0. Here the incoherent Hall conductivity, studied in [39] for a non-dynamical external magnetic field, is expected to be needed for matching the holographic results to magnetohydrodynamics. A second, and perhaps more interesting, continuation of our program is to consider the same setup in one additional dimension, allowing for an arbitrary angle θ between the magnetic field B and the wave-vector k. Finally, it would be important to better understand the relationship between our modified boundary conditions and the higher-forms bulk theories [11].…”

Wiedemann-Franz laws and Sl(2, ℤ) duality in AdS/CMT holographic duals and one-dimensional effective actions for them

“…8 Here, to match equations (3.32)-(3.34) we simply assumed that the frequency can be reinstated by a shift of 1/τ imp . The authors of [32] show that the correct ω dependence is captured by the higher order corrections in B, and that the hydrodynamic and holographic results match. It was also noted that conductivities, apart from σ Q also depend on another universal parameter σ H -the incoherent Hall conductivity.…”

“…More recently, the hydrodynamic derivation of the conductivities was generalized to arbitrary values of B in [32]. 8 Here, to match equations (3.32)-(3.34) we simply assumed that the frequency can be reinstated by a shift of 1/τ imp .…”

Die hard holographic phenomenology of cuprates

“…Similar incoherent terms were argued to appear in the other thermo-electric coefficients, α inc = -µσ inc /T andκ inc = µ 2 σ inc /T, which, however, cancel against each other in the zero-current coefficient κ. Recently, it was argued that similar terms must be introduced into the Hall components of the kinetic coefficients as well [59].…”