Conductivity Tensor in a Holographic Quantum Hall Ferromagnet

TL;DR

This paper computes the conductivities and entropy of a holographic quantum Hall ferromagnet, revealing phase transition effects that mimic features of integer quantum Hall systems, including a flattened Hall conductivity and entropy behavior.

Contribution

It introduces a holographic model that captures phase transition effects and conductivity features similar to quantum Hall phenomena, with detailed calculations of conductivities and entropy.

Findings

Hall conductivity shows a flattened dependence with a jump at the phase transition

Longitudinal conductivity exhibits features similar to 2D electron gases in quantum Hall regime

Low temperature entropy behavior indicates phase transition effects

Abstract

The Hall and longitudinal conductivities of a recently studied holographic model of a quantum Hall ferromagnet are computed using the Karch-O'Bannon technique. In addition, the low temperature entropy of the model is determined. The holographic model has a phase transition as the Landau level filling fraction is increased from zero to one. We argue that this phase transition allows the longitudinal conductivity to have features qualitatively similar to those of two dimensional electron gases in the integer quantum Hall regime. The argument also applies to the low temperature limit of the entropy. The Hall conductivity is found to have an interesting structure. Even though it does not exhibit Hall plateaux, it has a flattened dependence on the filling fraction with a jump, analogous to the interpolation between Hall plateaux, at the phase transition.