A holographic model of the quantum Hall effect

✍ Scribed by O. Bergman; N. Jokela; G. Lifschytz; M. Lippert

• Publisher: John Wiley and Sons
• Year: 2011
• Tongue: English
• Weight: 170 KB
• Volume: 59
• Category: Article
• ISSN: 0015-8208
• DOI: 10.1002/prop.201100007

✦ Synopsis

Abstract

We describe a holographic model of strongly coupled fermions in 2+1 dimensions based on a D7‐brane probe in the background of D3‐branes. The novel D7‐brane embedding is stabilized by turning on a certain worldvolume flux. We study the system at nonzero temperature and charge density, and in the presence of a background magnetic field. We show that Minkowski embeddings, which terminate above the horizon, describe a family of quantum Hall states with filling fractions that are parameterized by a single discrete parameter. The quantization of the Hall conductivity is a direct consequence of the topological quantization of the fluxes. When the magnetic field is varied relative to the charge density away from these discrete filling fractions, the embeddings deform continuously into black hole embeddings, which enter the horizon and describe metallic states.