Holographic Non-Fermi Liquid in a Background Magnetic Field

TL;DR

The paper investigates how a background magnetic field affects holographic 2+1D non-Fermi liquids by embedding a probe fermion in an extremal dyonic AdS$_4$ black hole. The magnetic field effectively rescales the fermion charge to $q_{\text{eff}} = q\sqrt{1 - h^2/3}$, yielding Landau-like level structure with discrete $L_n^2=2nqh$ and inducing de Haas–van Alphen–type oscillations, including a potential dissolution of the Fermi surface for positive mass. Key contributions include the separation of variables revealing Landau-level quantization, the demonstration of periodic spectral divergences as poles cross physical levels, and Onsager-like relations linking field periodicity to the Fermi-surface area. These results bridge holographic non-Fermi liquid behavior with familiar condensed-matter phenomena in magnetic fields and lay groundwork for exploring quantum Hall effects and finite-temperature extensions in holographic setups.

Abstract

We study the effects of a non-zero magnetic field on a class of 2+1 dim non-Fermi liquids, recently found in 0903.2477 by considering properties of a fermionic probe in an extremal AdS^4 black hole background. Introducing a similar fermionic probe in a dyonic AdS^4 black hole geometry, we find that the effect of a magnetic field could be incorporated in a rescaling of the probe fermion's charge. From this simple fact, we observe interesting effects like gradual disappearance of the Fermi surface and quasi particle peaks at large magnetic fields and changes in other properties of the system. We also find Landau level like structures and oscillatory phenomena similar to the de Haas-van Alphen effect.

Figures (3)

• Figure 1: Fig 5 of Faulkner:2009wj. The values of $k_F$ as a function of $q$ are shown by the solid lines for $m=0.4,m=-0.4,m=0$. The oscillatory region with imaginary $\nu_k$ is shaded. As we turn on a non-zero magnetic field $q$ changes to $q_{eff}=q\sqrt{1-\frac{h^2}{3}}$. From this diagram one can easily see what happens to the system.
• Figure 2: The poles of $\mathrm{Im}~\bar{\xi}$ at $\omega=-10^{-9}$, $m=0$ with different magnetic fields $h$ and $q_{ini}=1$: from right to left, $h=0.205,~0.39,~0.5,~0.7,~1.0,~1.4$ respectively.
• Figure 3: Oscillations in the susceptibility with varying magnetic field.