ModMax Electrodynamics and Holographic Magnetotransport

TL;DR

This work addresses magnetotransport in a strongly coupled 2+1D boundary theory by holographically coupling ModMax nonlinear electrodynamics to AdS gravity and introducing momentum relaxation. The authors derive exact dyonic black hole solutions and perform linear response analyses to obtain DC conductivities from horizon data, revealing a nonlinear modification of the Hall response while preserving some Maxwell-like scaling. They further show that momentum relaxation produces finite transport and yields Hall-angle and Nernst signals that resemble features seen in cuprate strange metals and high-$T_c$ superconductors, with the ModMax parameter $\gamma$ tuning characteristic temperatures. In the ultranonlinear regime, the bulk reduces to a magnetic stealth configuration atop AdS-Schwarzschild, driving distinctive transport behavior including a negative Nernst signal and exotic quasiparticle-dominated phases, highlighting nonlinear electrodynamics as a flexible tool to model complex quantum materials in holography.

Abstract

We study magnetotransport in a holographic model where ModMax nonlinear electrodynamics is coupled to Einstein anti--de Sitter gravity. To incorporate momentum relaxation, we introduce spatially linear free scalar fields that break translational symmetry, resulting in an anisotropic medium. Using linear response theory, we compute the DC conductivity matrix in the presence of an external magnetic field, expressing the conductivities in terms of horizon data. Our results demonstrate how the nonlinear ModMax parameter modifies charge transport, particularly influencing the Hall angle and Nernst signal. The nonlinear corrections introduce distinct deviations in both longitudinal and Hall conductivities while preserving the characteristic temperature scaling of strange metals, offering new insights into strongly coupled systems with nonlinear electromagnetic interactions. Notably, the Nernst signal reproduces that of high-$T_c$ cuprate superconductors showing a superconducting dome and a normal phase, with the ModMax deformation parameter tuning critical and onset temperatures. In the strongly nonlinear regime, we find evidence of an exotic state dominated by quasiparticle excitations in the dual material.

Figures (5)

• Figure 1: Free energy $G{\cal F}$ as a function of temperature for the black hole solution with $k=1\,, \ell=\sqrt{3}\,, e^{\gamma}Q^2=q_{\rm E}^2+q_{\rm M}^2=1.125\times 10^{-2}$ .
• Figure 2: The solid curves represent inversion curves with $Q=5$ , while the isenthalpic curves are shown in dotted, dashed, and dot-dashed for different values of $M$ . The left, center, and right plots correspond, respectively, to $k=-1,0,1$ .
• Figure 3: The tangent of the Hall angle as a function of the ModMax deformation parameter $\gamma$ , shown for various values of the normalized temperature $T/\mu$ , with the scalar intensity fixed at $\alpha = 10$ , the electromagnetic charges at $q_{\rm E}=1$ , $q_{\rm M}=0.5$, and the AdS radius at $\ell=1$ for all curves.
• Figure 4: Nernst signal as a function of the magnetic field for various values of the bulk parameters.
• Figure 5: Dependence of the Nernst signal on the temperature $T$ for various values of $\gamma$ , with fixed parameters $q_{\rm E} = 0.1$ , $q_{\rm M} = 0.1$ , and $\alpha = 0.3$ .