Magnetotransport and Complexity of Holographic Metal-Insulator Transitions

TL;DR

This paper investigates magnetotransport properties near a holographic metal-insulator transition, revealing universal scaling behaviors, phase diagram features, and spectral weight transfer, with implications for understanding complex transition dynamics.

Contribution

It introduces a minimal holographic model capturing universal features of metal-insulator transitions, including scaling laws and spectral weight transfer, without relying on detailed non-linear holographic specifics.

Findings

Resistivity scales with a single parameter T_0 near the transition.

Spectral weight shifts from low to high energies due to disorder.

Phase diagram constructed in temperature and disorder space.

Abstract

We study the magnetotransport in a minimal holographic setup of a metal-insulator transition in two spatial dimensions. Some generic features are obtained without referring to the non-linear details of the holographic theory. The temperature dependence of resistivity is found to be well scaled with a single parameter $T_0$, which approaches zero at some critical charge density $\rho_c$, and increases as a power law $T_0\sim|\rho-\rho_c|^{1/2}$ both in metallic $(\rho>\rho_c)$ and insulating $(\rho<\rho_c)$ regions in the vicinity of the transition. Similar features also happen by changing the disorder strength as well as magnetic field. By requiring a positive definite longitudinal conductivity in the presence of an applied magnetic field restricts the allowed parameter space of theory parameters. We explicitly check the consistency of parameter range for two representative models, and compute the optical conductivities for both metallic and insulating phases, from which a disorder-induced transfer of spectral weight from low to high energies is manifest. We construct the phase diagram in terms of temperature and disorder strength. The complexity during the transition is studied and is found to be not a good probe to the metal-insulator transition.