This grant supports theoretical research on the properties of superconductors, including the high temperature superconductors that continue to challenge our conventional understanding. Besides contributing to fundamental understanding of basic condensed matter physics, results from this research may impact technological applications of the high temperature superconductors.
A remarkable trio of experiments now point to the pseudogap state in underdoped cuprates as being a fluctuating nodal d-wave superconductor. Nernst effect measurements by the Princeton group indicate strong vortex fluctuations, far inside the region of true superconducting long-range order. STM observations of charge modulation in strongly underdoped samples agree with the expectation that such strong quantum vortex-antivortex fluctuations naturally generate a density-wave of Cooper pairs. Finally, recent heat transport experiments by Taillefer's group support the presence of nodal fermionic excitations even outside the superconducting state. Taken together, these experiments appear to characterize the pseudogap state as being a "superconductor," with nodes but without superconductivity, and prone to formation of two-dimensional modulated structures.
A nodal "2e" density-wave is precisely what the pseudogap state is in the theory of quantum fluctuating nodal d-wave superconductors developed by the principal investigator and his collaborators during the prior grant period. As singly quantized vortex-antivortex pairs unbind, the off-diagonal long-range order (ODLRO) of a superconductor is lost to a charge density-wave of Cooper pairs, and the system turns into a charge insulator. An exceptional feature of a nodal d-wave superconductor is that this loss of ODLRO does not imply simultaneous destruction of gapless nodes. The nodes remain protected by an emergent fermionic "chiral" symmetry and can be ultimately destroyed only through an additional quantum transition - strikingly, such a transition almost certainly leads to an antiferromagnet. Thus, the pseudogap remains a spin conductor, its low energy fermionic excitations exhibiting the Bogoliubov-deGennes chiral symmetry inherited from a nearby superconductor. The presence of these gapless spinful fermions testifies to the stiffness of the d-wave pairing amplitude - hence the pseudogap.
The main theme of the present project is the exploration of important "non-universal" properties of the effective theory of quantum phase fluctuating nodal superconductors. Such "non-universal" properties have a decidedly faint theoretical appeal but play a crucial role in making contact with the spectacular ongoing experimental effort. Issues like the precise microscopic pattern of the Cooper pair density-wave, the role of interlayer coupling, the effect of finite magnetic fields, the details of the phase diagram of the theory, etc., previously often dealt with in a few paragraphs, will now take center stage in an all-out effort to objectively assess the value of this theoretical description for the physics of cuprates and related superconductors.
