Pseudogap in a Magnetic Field: A Case of Quantum Vortex Liquid in a Corelated d-wave Superconductor

Recent experiments by the Princeton group provide a clear indication of enhanced superconducting fluctuations in the pseudogap state of underdoped cuprates. In addition to the giant Nernst effect, which testifies to the thermal vortex excitations, strong diamagnetic and ``vortex liquid-type'' responses at very low temperatures point to predominance of {\em quantum} phase fluctuations throughout the pseudogap regime. This is of much importance: while {\em all} superconductors exhibit thermal phase fluctuations, the quantum phase disorder -- leading to a non-superconducting ground state despite robust local pairing correlations -- is decidedly outside the reach of any BCS-like, weak-coupling style theory. I will introduce general aspects of the theory of quantum disordered, strongly correlated d-wave superconductors and will use the theory to sketch the phenomenology of quantum vortex-liquid in heavily underdoped cuprates.