Quantum fluctuation generated vortices, dual singular-gauge transformation, and zero-temperature transition from d-wave superconductor to underdoped regime

By extending the original Anderson singular-gauge transformation for static vortices to two mutual flux-attaching singular-gauge transformations for moving vortices, we derive an effective action describing the zero-temperature quantum phase transition from d-wave superconductor to underdoped regime. In this action, quantum fluctuation generated vortices couple to quasiparticles by a mutual statistical interaction with statistical angle θ=1/2 and a dynamic Doppler shift term. The vortices also interact with each other by long-range logarithmic interactions due to charge fluctuation. Neglecting the charge fluctuation first, we find that the mutual statistical interaction is exactly marginal. In the underdoped regime, the quasiparticles are described by (2+1)-dimensional QED; in the superconducting regime, they are essentially free. However, putting back the charge fluctuation changes the physical picture dramatically: both the dynamic Doppler shift term and the mutual statistical interaction become irrelevant short-ranged interactions on both sides of the quantum critical point. There are no spin-charge separation and no dynamic gapless gauge field in the Cooper-pair picture. The formalism developed at T=0 is applied to study thermally generated vortices in the vortex plasma regime near the finite temperature Kosterlitz-Thouless transition. The important effects of the AB phase scattering and the Doppler shift on angle resolved photoemission spectroscopy data are also briefly reviewed.