Quantum Criticality of d-Wave Quasiparticles and Superconducting Phase Fluctuations

We present finite temperature (T) extension of the (2+1)-dimensional QED (QED₃) theory of underdoped cuprates. The theory describes nodal quasiparticles whose interactions with quantum proliferated hc/2e vortex-antivortex pairs are represented by an emergent U(1) gauge field. Finite T introduces a scale beyond which the spatial fluctuations of vorticity are suppressed. As a result, the spin susceptibility of the pseudogap state is bounded by T² at low T and crosses over to ∼T at higher T, while the low-T specific heat scales as T², reflecting the thermodynamics of QED₃. The Wilson ratio vanishes as T→0; the pseudogap state is a “thermal (semi)metal” but a “spin-charge dielectric.” This non-Fermi liquid behavior originates from two general principles: spin correlations induced by “gauge” interactions of quasiparticles and fluctuating vortices and the “relativistic” scaling of the T=0 fixed point.