Seminar – Prof. Philip Phillips – University of Illinois at Urbana-Champaign

Beyond BCS: An Exact Model for Superconductivity and Mottness

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.  Part of the problem is
that the basic model for a Mott insulator, namely the Hubbard model is
unsolvable in any dimension we really care about.
 To address this problem, I will start by focusing on the overlooked
Z_2 emergent symmetry of a Fermi surface first noted by Anderson and
Haldane. Noting that Mott insulators break this emergent symmetry, I
show that the simplest model that suffices to describe
Mottness is the Hatsugai-Kohmoto model. This model will then be solved
exactly to reveal how superconductivity emerges in a doped Mott
insulator, thereby forming a new paradigm for superconductivity in the
copper-oxide superconductors.
[1] P. Phillips, L. Yeo, E. Huang, Nature Physics, 16, 1175-1180 (2020).