QED3 theory of pairing pseudogap in cuprates: From d-wave superconductor to antiferromagnet via "algebraic" Fermi liquid

TL;DR

This paper develops a QED$_3$-based theoretical framework to describe the pseudogap state in cuprate superconductors, linking d-wave pairing, strong correlations, and quantum vortex dynamics.

Contribution

It introduces a novel QED$_3$ effective theory for the pseudogap phase, connecting nodal quasiparticles and vortex unbinding to emergent gauge fields.

Findings

QED$_3$ describes the pseudogap state with Dirac fermions and gauge fields.

The theory predicts properties analogous to Fermi liquid behavior in the pseudogap phase.

Physical consequences of the QED$_3$ framework are discussed for cuprate superconductors.

Abstract

High-$T_c$ cuprates differ from conventional superconductors in three crucial aspects: the superconducting state descends from a strongly correlated Mott-Hubbard insulator, the order parameter exhibits d-wave symmetry and superconducting fluctuations play an all important role. We formulate a theory of the pseudogap state in the cuprates by taking the advantage of these unusual features. The effective low energy theory within the pseudogap phase is shown to be equivalent to the (anisotropic) quantum electrodynamics in (2+1) space-time dimensions (QED$_3$). The role of Dirac fermions is played by the nodal BdG quasiparticles while the massless gauge field arises through unbinding of quantum vortex-antivortex degrees of freedom. A detailed derivation of this QED$_3$ theory is given and some of its main physical consequences are inferred for the pseudogap state. We focus on the properties of symmetric QED$_3$ and propose that inside the pairing protectorate it assumes the role reminiscent of that played by the Fermi liquid theory in conventional metals.