Temperature Dependence of In-plane Resistivity and Inverse Hall Angle in NLED Holographic Model

Abstract: In the strange metal phase of the high-$T_{c}$ cuprates, it is challenging to explain the linear temperature dependence of the in-plane resistivity and the quadratic temperature dependence of the inverse Hall angle. In this paper, we investigate the temperature dependence of the in-plane resistivity and inverse Hall angle in the nonlinear electrodynamics holographic model developed in our recent work. Maxwell electrodynamics and Born-Infeld electrodynamics are considered. Both cases support a wide spectrum of temperature scalings in parameter space. For Maxwell electrodynamics, the T-linear in-plane resistivity generally dominates at low temperatures and survives into higher temperatures in a narrow strip-like manner. Meanwhile, the T-quadratic inverse Hall angle dominates at high temperatures and extends down to lower temperatures. The overlap between the T-linear in-plane resistivity and the T-quadratic inverse Hall angle, if occurs, would generally present in the intermediate temperate regime. The Born-Infeld case with $a>0$ is quite similar to the Maxwell case. For the Born-Infeld case with $a<0$, there can be a constraint on the charge density and magnetic field. Moreover, the overlap can occur for strong charge density.