Entropy and de Haas-van Alphen oscillations of a three-dimensional marginal Fermi liquid

TL;DR

This paper investigates de Haas-van Alphen oscillations in a three-dimensional marginal Fermi liquid near a quantum critical point, revealing breakdowns of traditional formulas and deriving modified expressions valid in non-Fermi liquid regimes.

Contribution

It introduces a new framework incorporating quantum critical effects into oscillation calculations, extending beyond the Lifshitz-Kosevich formula for marginal Fermi liquids.

Findings

Conventional oscillation formulas fail when correlation length exceeds cyclotron radius.

Quantum fluctuations significantly enhance the oscillatory part of the self-energy.

Derived modified expressions for entropy and magnetization oscillations in non-Fermi liquid regimes.

Abstract

We study de Haas-van Alphen oscillations in a marginal Fermi liquid resulting from a three-dimensional metal tuned to a quantum-critical point (QCP). We show that the conventional approach based on extensions of the Lifshitz-Kosevich formula for the oscillation amplitudes becomes inapplicable when the correlation length exceeds the cyclotron radius. This breakdown is due to (i) non-analytic finite-temperature contributions to the fermion self-energy (ii) an enhancement of the oscillatory part of the self-energy by quantum fluctuations, and (iii) non-trivial dynamical scaling laws associated with the quantum critical point. We properly incorporate these effects within the Luttinger-Ward-Eliashberg framework for the thermodynamic potential by treating the fermionic and bosonic contributions on equal footing. As a result, we obtain the modified expressions for the oscillations of entropy and magnetization that remain valid in the non-Fermi liquid regime.