This award supports theoretical research and education with the ambitious goal to formulate a consistent microscopic theory of the extraordinary phenomena which have been discovered in high temperature cuprate superconductors. The PI sees that besides the high superconducting transition temperatures, two new states of matter have been discovered in the cuprates: a strange normal metallic state with extraordinary but simply characterized properties, and a pseudogap phase in which the extrapolated normal ground state appears to have an anisotropic gap tied to the chemical potential. The PI will build on a microscopic approach which predicted a particular form of broken time-reversal symmetry in the pseudogap phase, and derived a quantum critical spectrum of the order parameter fluctuations, which leads to the phenomenological marginal Fermi-liquid consistent with the "strange metal" state, as well as couples to fermions with attraction in the d-wave pairing channel. The PI aims to solidify aspects of these developments and to attempt an understanding of aspects which are not understood. These include (i) verification of the analytic results for the quantum fluctuations by Monte Carlo calculations, (ii) inversion of the ARPES data to deduce the pairing spectrum to test the theory, (iii) understanding how the time-reversal breaking state observed in recent experiments necessarily leads to an anisotropic gap in the "pseudogap" state, as well as other issues relevant to experiment. The PI aims to achieve a firm enough theory backed by experimental results and with clear and falsifiable predictions so that a consensus in the important field of cuprate high temperature superconductivity can be achieved. The PI will also take a close look at the burgeoning experimental results on the newly discovered Fe-Pnictides and formulate a model for their understanding.
NON-TECHNICAL SUMMARY This award supports theoretical research and education with the ambitious goal to formulate a consistent theory of the extraordinary phenomena which have been discovered in high temperature cuprate superconductor materials. Apart from the persistence of superconductivity to much higher temperatures than the other superconducting materials known at the time of the discovery of the cuprates, the cuprate materials exhibit a host of interesting puzzles including the nature of the unusual metallic states that give way to the superconducting state as the temperature is lowered. The PI will build on his recent controversial ideas that have support in the experimental data. His work may lead to new insights into high temperature superconductivity and how to discover new materials that are superconducting at much higher temperatures, perhaps room temperature. In the superconducting state, superconductors can carry electric power without dissipation. A room temperature superconductor would enable efficient power transmission and save energy.
The discovery of high temperature Superconductivity in a ceramic compound of Copper, Oxygen and other elements in 1987 was one of the most important discoveries of the later half of the 20-th century. On the one hand it opened up hopes of a new technology with imapact similar to what the discovery of transistors had earlier; on the other it called for a re-examination of some of the most important paradigms in Physics. It has led to an unprecedented world wide effort in exploration and understanding of the observed phenomena which has brought to fore many discoveries in this and related fields of condensed matter physics and to the growth and nurturing of new idea that are revolutionizing Physics as well as related aspects in Chemistry. The reigning paradigm in Physics has been the "quasi-particle" concept, that there is a one to one correspondence between the properties of strongly interacting particles and non-interacting particles. This paradigm fails in high temperature superconductors and many other compounds, subsequently discovered. It is understood that this is due to quantum fluctuations. Understanding the nature and variety of quantum fluctuations has therefore become the central problem. This also governs the major activities in elementary particle physics and questions of the origin of the Unvierse in cosmology. These fields have had frutiful interactions in which high temperature superconductivity phenomena has played an important role. This project began with two earlier realizations of the Principal Investigator (PI). One is that the temperature region above superconductivity, the quantum fluctuations though short-ranged in space are scale-invariant in time. Scale-invariance in time means that if one observes the properties through a telescope with varying magnifications in time, it looks the same at any different magnification. The other is that such fluctuations are the fluctuations in time of a new phase of matter in which loops of currents organize themselves throughout the compounds in a particular pattern. Such an organization breaks the symmetry of the arrow of time which holds usually in microscopic phenomena in the absence of dissipation. The experimental signatures of the loops of currents is elusive but following the PI's proposal, they have been looked for by a variety of techniques in many different laboratories around the world and found systematically. In this project, the consequences of these discoveries for the properties of high temperature superconductors in various parts of their phase diagram were explored. The proposed necessary quantum fluctuations were shown to arise from the loop-currents due to quantum-fluctuations which fluctuate the arrow of time locally through topological objects termed "warps". Warps are fluctuations which flip the arrow of time. These fluctuations were shown to promote the observed high temperature superconductivity. Experiments which probe the change the energy and momentum of electrons through interactions with such fluctuations were proposed and are being analyzed to test the details of this hypothesis. Experiments which probe the change in the propagation characteistic of light when such loop-currents flow have been analyzed. These and the experiments discovering the loop currents revealed several unanticipated features whose understanding have led to a deeper insight and new predictions for experiments. Further calculations to confirm and quantify the parameters for the existence of the predicted order and the fluctuations have also been done. It is expected that through the completion of this and subsequent project a complete and unique understanding of the high temperature superconducting phenomena will be achieved. The understanding of quantum fluctuations has already led to investigations in related fields in Physics.