Superconductivity, electronic correlations, and disorder: the Hirschfeld group attacks problems at the nexus of these three areas. Research is funded by the US Department of Energy ("Theory of novel superconductors") and the National Science Foundation ("Disorder and the emergence of inhomogeneous phases in correlated electron systems").
The Meissner effect, where magnetic field is expelled from the interior of a superconductor, is one of the fundamental characteristics of superconductivity. Here, a crystal of the cuprate supercconductor YBCO is levitated above a magnet.
One of the great goals of condensed matter physics
is to what causes superconductivity in its various forms. While this is a 100-year old problem,
partially solved by Bardeen, Cooper and Schrieffer in 1957, the field continues today as
vibrantly and actively as ever. on the fiftieth anniversary, in 1961, when Brian Pippard gave his
famous “The Cat and the Cream” speech to an audience at IBM, claiming that (four years
after the publication of the BCS theory) the essential fundamental problems in
low-temperature physics had been solved. All that remained, he argued, was for the
giant industrial laboratories of the day to apply these ideas, lapping up what “cream”
remained. Today one is confronted with a very different impression: the industrial
labs have retired from the scene, and university research drives progress.
Hardly a dying field, superconductivity today is inspired by the continuing
discoveries of new materials, including heavy fermions, cuprates, ruthenates,
borides, fullerides, organics, MgB2 and, most recently, Fe-based materials.
Moreover, in almost every case the discovery of a new class of superconductors has forced theorists to reexamine cherished theoretical paradigms. Indeed, Pippard’s speech encouraged Phil Anderson to distill his own ideas as to why emergent quantum phenomena like superconductivity mean “more is different”, and are as “fundamental” to physics as elementary particles.
Map of local density of states modulations in cuprate superconductor BSCCO imaged by scanning tunneling microscopy (STM), thought to be associated with recently discovered charge order in underdoped cuprates.
The Landau Fermi liquid paradigm has guided condensed matter physics for sixty years, allowing one to understand why the Bloch 1-electron theory accounts well for the electronic properties of crystalline solids despite the fact that electron-electron interactions are of the same order as kinetic energies. The Landau theory can break down in the presence of strong local Coulomb interactions, and such solids must be understood within the alternative Mott-Hubbard paradigm. These electronic correlation effects are essential to the understanding of unconventional superconductivity, where the attraction between electrons in a Cooper pair arises from bare repulsive Coulomb forces. Strongly correlated oxides and related "quantum materials" exhibit a variety of competing ground states and represent a fundamental challenge of condensed matter physics.
STM map of energy gap size, varying from point to point by nearly a factor of 2 on the surface of BSCCO. This effect is believed to be caused by strong electronic correlations and oxygen defect disorder. The red dots represent the locations of O dopant atoms which are also imaged.
Condensed matter physics is based on the Bloch theory of periodic systems, and a major frontier consists of understanding the effect of disorder on electronic wavefunctions. While for non- or weakly interacting metals the Anderson theory of localization provides an adequate approach to disorder problems, there are many fundamental open questions about the role of disorder in the presence of strong correlations and low dimensions. One of them under active investigation in the Hirschfeld group is how disorder mediates the competition between different broken symmetry ground states, particularly superconductivity, antiferromangetism, and electronic nematicity.