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Fomichev, Stepan Olegovich

University of British Columbia

Motivated by the success of the momentum average (MA) approximation for the single-polaron and bipolaron cases, in this dissertation we pursue the first generalization of this technique to the case of weakly-doped insulators beyond the Migdal limit. In search of a suitable starting point, we investigate the ground states of a variety of model Hamiltonians, inspired by real materials such as rare-earth nickelates, polyacetylene, barium bismuthates, and buckminsterfullerene. Our study of the ground state of the 2D rare-earth nickelate sheet shows that it exhibits cuprate-like orbital polarization unimpeded by weak to moderate electron-phonon coupling. This lends further support to the proposal for cuprate-like superconductivity in nickelate thin films and heterostructures. Investigating polyacetylene leads us to develop a semi-analytical technique that can be used to account for zero-point lattice energy in determining the equilibrium geometry of any crystal. The study of a simplified, one-dimensional model of buckminsterfullerene results in the first generalization of MA to a system with two polaron clouds, and a phonon-driven mechanism for exciton dissociation that could be responsible for photocurrent generation in these materials. Because both the nickelates and polyacetylene turn out to be too complex as starting points for MA generalization, we focus on a simplified, s-p chain model of the barium bismuthates. We ultimately succeed in generalizing MA for this band insulator – the first application of its kind. We compare the results to those from determinant quantum Monte Carlo to establish the accuracy of the MA results (with the MA results obtained at lower computational cost). Finally, we share in the development of the first open-sourced Python package implementing automatic MA equation generation via the GGCE method, which allows MA-style methods to be easily used by non-experts – and is expected to expand in the coming years, providing access to many more MA-style methods in the future.

Text

2023-09-08

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/85883

Physics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/