High-temperature superconductivity in the cuprates remains an unsolved
problem because the cuprates start off their lives as Mott insulators in
which no organizing principle such a Fermi surface can be invoked to
treat the electron interactions. Consequently, it would be advantageous
to solve even a toy model that exhibits both Mottness and
superconductivity. In 1992 Hatsugai and Khomoto wrote down a
momentum-space model for a Mott insulator which is safe to say was
largely overlooked, their paper garnering just 21 citations (6 due to
our group). I will show exactly[1] that this model when appended with a
weak pairing interaction exhibits not only the analogue of Cooper's
instability but also a superconducting ground state, thereby
demonstrating that a model for a doped Mott insulator can exhibit
superconductivity. The properties of the superconducting state differ
drastically from that of the standard BCS theory. The elementary
excitations of this superconductor are not linear combinations of
particle and hole states but rather superpositions of doublons and
holons, composite excitations signaling that the superconducting ground
state of the doped Mott insulator inherits the non-Fermi liquid
character of the normal state. Additional unexpected features of this
model are that it exhibits a superconductivity-induced transfer of
spectral weight from high to low energies and a suppression of the
superfluid density as seen in the cuprates.
[1] https://www.nature.com/articles/s41567-020-0988-4.
Professor Philip Phillips received his bachelor's degree from Walla Walla
College in 1979, and his Ph.D. from the University of Washington in 1982.
After a Miller Fellowship at Berkeley, he joined the faculty at Massachusetts
Institute of Technology (1984-1993). Professor Phillips came to the University
of Illinois in 1993. Professor Phillips is a theoretical condensed matter
physicist who has an international reputation for his work on transport in
disordered and strongly correlated low-dimensional systems. He is the inventor
of various models for Bose metals, Mottness, and the random dimer model, which
exhibits extended states in one dimension, thereby representing an exception
to the localization theorem of Anderson's.
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