A theorem of Kohn applied to quantum oscillations in Cuprates

TL;DR

This paper applies Kohn's theorem and the Gell-Mann and Low theorem to demonstrate that quantum oscillations in cuprates are consistent with Fermi liquid behavior, providing a rigorous theoretical justification.

Contribution

It offers a non-perturbative proof that quantum oscillations in cuprates reflect Fermi liquid properties, extending the theoretical understanding of these materials.

Findings

Quantum oscillation frequencies match non-interacting models.

Quantum oscillations indicate Fermi liquid behavior in cuprates.

The Gell-Mann and Low theorem applies to cuprates under certain conditions.

Abstract

In this note I apply a theorem of Kohn to quantum oscillations in cuprates. I show that when combined with Gell-Mann and Low theorem, there is rigorous justification of quantum oscillations as in a Fermi liquid for cuprates. The Gell-Man-Low theorem is not perturbative, and applies more generally as long as the adiabatic evolution from an isolated non-degenerate state is the case. Oscillation frequencies are identical to the non-interacting problem. Thus, quantum oscillations protect the Fermi liquid and is in turn protected by it. This is not to imply that other properties of the cuprates that do not have a gap in the spectrum could not exhibit non-Fermi liquid behavior, for example, angle resolved photoemission spectroscopy.