Quantum oscillations and criticality in a fermionic and bosonic dimer model for the cuprates

TL;DR

This paper models quantum oscillations in cuprate superconductors using a fermionic and bosonic dimer system, linking observed mass divergence and superconducting pairing to a van Hove singularity at a quantum critical point.

Contribution

It introduces a dimer model that explains quantum oscillations and criticality in cuprates, connecting experimental observations with theoretical predictions of a van Hove singularity.

Findings

Good qualitative agreement with experimental effective masses.

Identification of a van Hove singularity at the quantum critical point.

Maximum d-wave pairing amplitude near the van Hove point.

Abstract

We study quantum oscillations for a system of fermionic and bosonic dimers and compare the results to those experimentally observed in the cuprate superconductors in their underdoped regime. Based on gauge invariance, we argue that the charge carriers obey the Onsager quantization condition and quantum oscillations take on a Lifshitz-Kosevich form. We obtain the effective mass and find good qualitative agreement with experiments if we tune the model to the point where the observed mass divergence at optimum doping is associated to a van Hove singularity at which four free-dimer Fermi pockets touch pairwise in the interior of the Brillouin zone. The same van Hove singularity leads to a maximum in the d-wave superconducting pairing amplitude when anti-ferromagnetic interactions are included. Our combined results therefore suggest that a quantum critical point separating the underdoped and overdoped regimes is marked by the location of the van Hove saddle point in the fermionic dimer dispersion.