High temperature superconductivity

The microscopic mechanism for high temperature superconductivity is one of foremost unsolved problems in solid state physics. A clear understanding of this mechanism may lead to the design of new materials which exhibit superconductivity at room temperature. This would lead to a technological revolution rivaling the semiconductor and the laser.

The central question in this field is the nature of the, parent, non-Fermi-liquid metallic state of a strongly interacting electron gas from which superconductivity emerges. This parent state differs from that of ordinary superconductors in a highly fundamental way. One aspect of the unconventional nature of the parent metal is the appearance of antiferromagnetism at very low charge carrier concentration and the disappearance of this magnetic state with increasing carrier concentration. Recently, our work has revealed the existence of  topological magnetic solitons in such an electron gas as well as a novel magnetic phase of these systems, which we refer to as a  spin-flux phase. When electrons are added to this system, this background magnetic state causes the spin and the charge of the electrons to separate and become bound to magnetic vortex solitons. These vortex solitons are the 2-d analogues of domain wall solitons in 1-d polyacetylene. They induce mid-gap electronic levels in the Mott-Hubbard charge transfer gap . In this state the electron gas no longer acts as a Fermi liquid, in agreement with experiments. The appearance of these solitons also leads to the observed disappearance of long range antiferromagnetic order in the spin background. We are developing a microscopic theory of the anomalous metallic phase and superconducting phase of the high temperature cuprate superconductors based on these concepts. Our current work involves the calculation of the Hartree-Fock energies of various magnetic solitons, the determination of the spin, charge, and statistics of these solitons, and the nature of the thermodynamic phases formed by a finite density of these solitons. We are studying the linear and nonlinear response of charged and uncharged to solitons to external electromagnetic fields. A detailed comparison of our model with experimentally observed magnetic, optical, and electronic properties of high temperature superconducting materials is being performed.