Solution of mass/gap equations for strong velocity anisotropy in the QED3 theory of underdoped 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_Δ) 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.