Doped Mott Hamiltonians

The cuprates, known to superconduct at exceptionally high temperatures when they are doped with holes, all descend from parent compounds that are standard Mott insulators. Because conductivity in these materials is dominated by transport within the copper-oxide planes, we focus our attention on the electronic structure of a single copper-oxide plane. These are well-described at low temperatures by the 2d Hubbard model, which, over the past sixty years, has been largely immune to analytic treatment in the physically relevant parameter regime. A simplification of the 2d Hubbard model is therefore in order, if we are to understand the microscopic basis for high-temperature superconductivity in the cuprates. While phase transitions around the Mott insulator lack a symmetry-based description, their phases are characterized by the spectral features associated with Mottness. These include a separation of spectral weight into upper and lower Hubbard bands, a Luttinger surface of zeros in the single-electron propagator, and spectral weight transfer from high to low energies. In this thesis, we turn from 2d Hubbard to the Hatsugai-Kohmoto (HK) model, which retains the features of Mottness while providing analytic traction. For instance, we can calculate all important physical observables as well as the finite- and zero-temperature state. In chapter 5, we examine entanglement and entropy across the interaction-driven metal-insulator transition in the HK model, finding features that distinguish the HK metal from Fermi liquid-like band metals. In chapter 6, we find that the HK metal is unstable to superconductivity and proceed to study a mean field theory of this superconducting phase. This superconductor displays a number of features found in the cuprates. These include Bogoliubov-like electronic excitations that descend from the HK metal and the appearance of a color change (i.e. the transfer of spectral weight from high to low energies brought about by the onset of superconductivity). Overall we find that this simple Hamiltonian can model coarse spectral features of the Mott insulating, metallic, and superconducting phases of the underdoped cuprates. Its simplicity provides a clear view of the microscopics that emerge as this doped Mott system and its superconducting instability.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Physics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2023

Author dc:creator

• Yeo, Luke

Contributors dc:contributor

• Phillips, Philip W
• Clark, Bryan
• DeMarco, Brian
• Bradlyn, Barry

• High-temperature Superconductivity
• Mottness
• Strongly-correlated Electrons

Statement dc:rights

• Copyright 2023 Luke Yeo

Language dc:language

en, eng

Handle dc:identifier

https://hdl.handle.net/2142/121389

OAI record oai:identifier

https://www.ideals.illinois.edu/oai-pmh?verb=GetRecord&metadataPrefix=etdms&identifier=oai%3Awww.ideals.illinois.edu%3A2142%2F121389