Path integral methods for polarons in real materials
File(s)
Author(s)
Martin, Bradley
Type
Thesis
Abstract
In this thesis, I develop theoretical methods for modelling polaron quasiparticles in semiconductors by extending Feynman's variational path integral approach. Polarons—quasiparticles formed by electron-phonon interactions—are critical for understanding charge transport in materials with significant electron-phonon coupling. Using Feynman's variational approximation (FVA) for the Fröhlich polaron. I present a non-perturbative framework to model polaron dynamics in materials with complex phonon interactions.
A key contribution is generalising the material action to include multiple phonon modes, reflecting realistic phonon spectra in modern materials. This framework extends to the Holstein polaron, anisotropic effective mass, and many-body systems. I generalise the trial path integral action to couple electrons with multiple fictitious spring-mass particles and introduce an extended Feynman-Jensen inequality, incorporating higher-order cumulant corrections for improved self-energy and mobility calculations across various coupling regimes.
Polaron charge-carrier mobility and optical conductivity are computed using the FHIP approximation and extended to temperature- and frequency-dependent models for multimode Fröhlich and Holstein polarons. These results are validated against Diagrammatic Monte Carlo simulations.
Numerical results are obtained using PolaronMobility.jl, an open-source Julia package I co-developed. It enables high-throughput screening of polar semiconductors and is demonstrated on methylammonium lead halide perovskites and rubrene organic crystals.
Finally, I conduct high-throughput predictions for polaronic properties of 1,268 materials from the Materials Project and Liège databases, identifying candidates for high-mobility applications based on parameters like effective mass, zero-point renormalisation energy, and room-temperature mobility.
A key contribution is generalising the material action to include multiple phonon modes, reflecting realistic phonon spectra in modern materials. This framework extends to the Holstein polaron, anisotropic effective mass, and many-body systems. I generalise the trial path integral action to couple electrons with multiple fictitious spring-mass particles and introduce an extended Feynman-Jensen inequality, incorporating higher-order cumulant corrections for improved self-energy and mobility calculations across various coupling regimes.
Polaron charge-carrier mobility and optical conductivity are computed using the FHIP approximation and extended to temperature- and frequency-dependent models for multimode Fröhlich and Holstein polarons. These results are validated against Diagrammatic Monte Carlo simulations.
Numerical results are obtained using PolaronMobility.jl, an open-source Julia package I co-developed. It enables high-throughput screening of polar semiconductors and is demonstrated on methylammonium lead halide perovskites and rubrene organic crystals.
Finally, I conduct high-throughput predictions for polaronic properties of 1,268 materials from the Materials Project and Liège databases, identifying candidates for high-mobility applications based on parameters like effective mass, zero-point renormalisation energy, and room-temperature mobility.
Version
Open Access
Date Issued
2024-10-03
Date Awarded
01/02/2025
Advisor
Frost, Jarvist Moore
Nelson, Jenny
Sponsor
Engineering and Physical Sciences Research Council
Grant Number
2446070
Publisher Department
Physics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)