Holographically smeared Fermi surface: Quantum oscillations and Luttinger count in electron stars

TL;DR

This paper studies a holographic model of strongly interacting matter with an electron star, revealing non-Fermi liquid behavior with quantum oscillations that deviate from Luttinger theorem but can be explained by smeared fermionic excitations.

Contribution

It demonstrates that electron stars exhibit Kosevich-Lifshitz quantum oscillations and introduces a field theory explanation for the Luttinger count in non-Fermi liquids.

Findings

Quantum oscillations follow Fermi liquid form in electron stars.

Fermi surface area does not obey simple Luttinger theorem.

Luttinger count is recovered via smeared fermionic excitations.

Abstract

We apply a small magnetic field to strongly interacting matter with a gravity dual description as an electron star. These systems are both metallic and quantum critical at low energies. The resulting quantum oscillations are shown to be of the Kosevich-Lifshitz form characteristic of Fermi liquid theory. It is seen that only fermions at a single radius in the electron star contribute to the oscillations. We proceed to show that the Fermi surface area extracted from the quantum oscillations does not obey the simplest statement of the Luttinger theorem, that is, it is not universally proportional to the total charge density. It follows that our system is a non-Fermi liquid that nonetheless exhibits Kosevich-Lifshitz quantum oscillations. We explain how the Luttinger count is recovered via a field theoretic description involving a continuum of `smeared' fermionic excitations.