NODAL LIQUID THEORY OF THE PSEUDO-GAP PHASE OF HIGH-T-C SUPERCONDUCTORS

We introduce and study the nodal liquid, a novel zero-temperature quan tum phase obtained by quantum-disordering a d-wave superconductor. It has numerous remarkable properties which lead us to suggest it as an e xplanation of the pseudo-gap state in underdoped high-temperature supe rconductors. In the absence of impurities, these include power-law mag netic order, a T-linear spin susceptibility, nontrivial thermal conduc tivity, and two-and one-particle charge gaps, the latter evidenced, e. g. in transport and electron photoemission (which exhibits pronounced fourfold anisotropy inherited from the d-wave quasiparticles). We use a (2 + 1)-dimensional duality transformation to derive an effective fi eld theory for this phase. The theory is comprised of gapless neutral Dirac particles living at the former d-wave nodes, weakly coupled to t he fluctuating gauge field of a dual Ginzburg-Landau theory. The nodal liquid interpolates naturally between the d-wave superconductor and t he insulating antiferromagnet, and our effective field theory is power ful enough to permit a detailed analysis of a panoply of interesting p henomena, including charge ordering, antiferromagnetism, and d-wave su perconductivity. We also discuss the zero-temperature quantum phase tr ansitions which separate the nodal liquid from various ordered phases.