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

TL;DR

The paper investigates how strong interactions at finite density manifest Fermi-surface physics within a holographic electron-star framework. By applying a small magnetic field, the authors show that quantum oscillations follow the Kosevich-Lifshitz form, but the Fermi-surface area inferred from these oscillations does not scale universally with the total charge, signaling a non-Fermi-liquid despite FL-like oscillations. They identify that only fermions at a specific bulk radius $r_\star$ contribute to the oscillations, while the full charge is carried by a continuum of smeared fermionic excitations distributed over the bulk, which reconciles the Luttinger count through an effective field theory of smeared fermions with a Landau-band structure. The work thus provides a concrete mechanism for Luttinger-count violations in holographic metals and links the IR scaling via the dynamical exponent $z$ to Landau damping, offering a bridge to fractionalized Fermi-liquid concepts and non-Fermi-liquid quantum criticality.

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.

Figures (3)

• Figure 1: The electron star. The field theory charge density is given by the bulk electric field, which is sourced entirely by the fermion fluid. Quantum oscillations are due to fermions at a single radius in the star. The quantum critical region emerges due to screening of the electric field by the fermion fluid.
• Figure 2: Radius contributing to quantum oscillations over the radius of the electron star. Larger $r_\star/r_s \geq 1$ is the interior of the star. From top to bottom, curves have $\hat{m} = 0.07, 0.36$ and $0.7$. We are characterising the solutions by their IR scaling exponent $z$ rather than $\hat{\beta}$.
• Figure 3: The 'Luttinger ratio' of the Fermi surface area to charge density (left) and the effective quasiparticle mass over the chemical potential (right) as a function of IR scaling exponent $z$. From left to right, curves have $\hat{m} = 0.07, 0.36$ and $0.7$.