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 T0, which approaches zero at some critical charge density ρc, and increases as a power law T0∼ |ρ − ρc|1/2 both in metallic (ρ > ρc) and insulating (ρ < ρc) 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.
Highlights
We study the magnetotransport in a minimal holographic setup of a metalinsulator transition in two spatial dimensions
In the framework of effective holographic theories for condensed matter we have studied a minimal example of a metal-insulator transition that can be driven by disorder, charge density as well as magnetic field
We have investigated magnetotransport in a minimal holographic setup of a two dimensional metal-insulator transition and uncovered some interesting features, shedding light on this interesting transition and the physical mechanism that drives it
Summary
We introduce the minimal holographic theory of metal-insulator transition. From an effective field theory point of view, such setup provides a holographic metal-insulator transition as minimal as possible, because there are no more dynamical ingredients in the dual field theory other than the translation breaking and the charge sector. While V (X) does not couple directly to the charge carriers, Y (X) captures the effects from charged impurities and is important to realize a metal-insulator transition. More general models were introduced in [28, 29], where higher derivative corrections to an effective holographic action of homogeneous disorder have been discussed in absence of magnetic field. We will fix the gravitational constant, the charge unit and the AdS radius to one, i.e. κN = e = L = 1
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