Landau Levels, Magnetic Fields and Holographic Fermi Liquids

TL;DR

This paper investigates the spectral function of a probe fermion in a holographic setup with magnetic fields, revealing an infinite family of quasiparticle peaks corresponding to Landau levels, and analyzing their properties at strong coupling.

Contribution

It introduces a detailed analysis of Landau levels in holographic Fermi liquids, comparing two classes of solutions and exploring their quasiparticle spectra at zero temperature.

Findings

An infinite family of quasiparticle peaks associated with Landau levels.

Scaling relations for Fermi energy with Landau level index and magnetic field.

Well-behaved dispersion patterns for quasiparticles at large Landau level index.

Abstract

We further consider a probe fermion in a dyonic black hole background in anti-de Sitter spacetime, at zero temperature, comparing and contrasting two distinct classes of solution that have previously appeared in the literature. Each class has members labeled by an integer n, corresponding to the n-th Landau level for the fermion. Our interest is the study of the spectral function of the fermion, interpreting poles in it as indicative of quasiparticles associated with the edge of a Fermi surface in the holographically dual strongly coupled theory in a background magnetic field H at finite chemical potential. Using both analytical and numerical methods, we explicitly show how one class of solutions naturally leads to an infinite family of quasiparticle peaks, signaling the presence of a Fermi surface for each level n. We present some of the properties of these peaks, which fall into a well behaved pattern at large n, extracting the scaling of Fermi energy with n and H, as well as the dispersion of the quasiparticles.