Quantum criticality of d-wave quasiparticles and superconducting phase fluctuations

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We present finite temperature extension of the QED₃ theory of underdoped cuprates. The theory describes nodal quasiparticles whose interactions with quantum proliferated vortex-antivortex pairs are represented by an emergent U(1) gauge field. Finite temperature introduces a scale beyond which the long wavelength fluctuations in the spatial components 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 electronic specific heat scales as T², reflecting the thermodynamics of QED₃. The Wilson ratio vanishes as T→ 0. 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.