Solution of mass/gap equations for strong velocity anisotropy in the QED3 theory of underdoped cuprates

TL;DR

This paper investigates how strong velocity anisotropy affects dynamical mass generation in an effective QED3 model of underdoped cuprates, revealing a high critical fermion number and implications for spin density wave formation.

Contribution

It provides the first analysis of the impact of strong velocity anisotropy on dynamical mass generation in QED3 for underdoped cuprates, extending previous isotropic models.

Findings

Critical fermion number N_c > 100 for anisotropic velocities.

Dynamical mass solutions are consistent at N=2 and N=100.

Implications for spin density wave formation in cuprates.

Abstract

The low-lying excitations at the nodes of the d-wave gap in the normal state for underdoped cuprates, close to the superconducting phase transition, may be described by an effective QED3 theory. There are three characteristic velocities: v_F, v_Delta and c. For v_Delta=v_F=c, the model reduces to N-flavour QED3. Here, in the isotropic limit, for N<N_0c, a critical number of fermions, a dynamical mass is generated which corresponds to the formation of a spin density wave. We study the effects of strong velocity anisotropy (v_F \neq v_\Delta) on dynamical mass generation. Solutions are given for the dynamical mass at both N=2 and N=100, and so we show that the critical number of fermions N_c>100. However, we argue that N_c=N_0c, when we go beyond the approximations used to derive our mass gap equations. We expect, though, that our solution for N=2 is roughly correct, at low momentum, for large enough anisotropies. Implications and possible extensions to this work are also discussed.