Quantum criticality of d-wave quasiparticles and superconducting phase fluctuations

Abstract

We present finite temperature extension of the QED$_3$ 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 $T^2$ at low T and crosses over to $\sim T$ at higher $T$, while the low-$T$ electronic specific heat scales as $T^2$, reflecting the thermodynamics of QED$_3$. The Wilson ratio vanishes as $T\to 0$. 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.