Anisotropic Fermi surface from holography

TL;DR

This paper uses holographic methods to study anisotropic Fermi surfaces in a charged black brane background, revealing anisotropic and isotropic behaviors depending on momentum directions, and confirming thermoelectric bounds.

Contribution

It introduces a detailed analysis of probe fermions in an anisotropic holographic setup, highlighting the shape of Fermi surfaces and thermoelectric properties.

Findings

Fermi surface is anisotropic when momentum has components along the anisotropic direction.

Fermi surface remains isotropic when both momenta are perpendicular to the anisotropic direction.

The system obeys the conjectured bounds for thermoelectric diffusion constants.

Abstract

We investigate the probe holographic fermions by using an anisotropic charged black brane solution. We derive the equation of motion of probe bulk fermions with one Fermi momentum along the anisotropic and one along the isotropic directions. We then numerically solve the equation and analyze the properties of Green function with these two momentums. We find in this case the shape of Fermi surface is anisotropic. However, for both Fermi momentums perpendicular to the anisotropic direction, the Fermi surface is isotropic. We verify that our system obeys the recently conjectured bound for thermoelectric diffusion constants for the stable branch of the black brane solutions.