Optical excitations and disorder in two-dimensional topological insulators

TL;DR

The thesis addresses how optical excitations reveal topological properties in 2D insulators and how disorder affects these phases. It develops fast tight-binding based methods to solve the Bethe-Salpeter equation for excitons, validates them on hBN and MoS$_2$, and demonstrates a topological photovoltaics mechanism via bulk-edge exciton dissociation in Bi(111) nanoribbons. It then shifts to disorder, outlining Berry-based invariants, Wilson loops, and entanglement-spectrum diagnostics, and introduces deep learning to classify disordered topological phases from entanglement data. The work highlights how excitonic physics in TIs can enable photovoltaics and how topology endures under disorder with practical classification tools, advancing both fundamental understanding and computational capabilities. Overall, the study provides concrete methodologies and benchmarks for modeling excitons in 2D TI materials, and introduces ML-assisted topology detection in disordered systems with potential for material design and experimental guidance. $E_X$ and spectral properties are central throughout, as are the TB-based exciton kernels and the interplay between bulk and edge states in topological contexts.$

Abstract

Topological phases of matter have garnered significant interest over the past two decades for two main reasons: their identification, via topological invariants, relies on the quantum geometry of the Bloch states, bringing attention to an aspect of electronic band structure overlooked up to their discovery. Secondly, these classes of materials present electronic states with unusual properties, leading to exotic phenomena and making them relevant for potential applications. In this thesis we explore both fundamental and technological aspects of the first discovered topological phase: the topological insulator. To this end, we consider different models of topological insulators with a particular emphasis on Bismuth compounds, evaluating their viability for photovoltaic applications, and separately, the impact of structural disorder on their properties.

Figures (104)

• Figure 1: (a) Feynman diagram showing the main contribution to the linear optical conductivity $\sigma_{ab}(\omega)$ in terms of free electron-hole pairs. (b) Band diagram illustrating the process of excitation of an electron-hole pair via absorption of a photon (solid lines) and deexcitation via emission (dashed lines). (c) Feynman diagram showing one of the contributions to the second-order conductivity $\sigma_{abc}(2\omega;\omega,\omega)$ for the specific case of second-harmonic generation. (d) Band diagram depicting the process of second-harmonic generation, where an electron-hole pair is excited to a higher conduction band via absorption of two photons. The indices $(a,b,c)$ denote light polarization, while the indices $(m,n,r)$ denote the band indices including momenta $\mathbf{k}$, and $\omega, \omega'$ are frequencies. Feynman diagrams adapted from parker2019.
• Figure 2: (a) Feynman diagram showing the main contribution to the linear optical conductivity $\sigma_{ab}(\omega)$ in terms of the exciton propagator $L(\omega)$, i.e. considering electron-hole interactions. (b) Band diagram illustrating the excitation of an exciton via absorption of a photon (solid line) and its deexcitation via photon emission (dashed line). (c) Schematic representation of an exciton in a crystal lattice, where the interacting electron-hole pair behaves similarly to a hydrogen atom.
• Figure 3: (Left) Absorption spectrum of bulk silicon, as obtained from DFT (RPA), GW-RPA and the BSE (excitons). The red points correspond to the experimental data, obtained from absorption_silicon_exp. Plot by Francesco Sottile, extracted from sottile_thesis. (Right) Absorption spectrum of LiF. The solid line corresponds to the BSE calculation, while the dashed one is without electron-hole excitations. The dots denote the experimental data, obtained from Roessler67. Extracted from Rohlfing1998.
• Figure 4: Spectral diagram showing the usual energies for bound excitons (in-gap states) and continuum excitons (beyond the gap).
• Figure 5: Zero and first order contributions to the particle-hole Green's function $G^{\text{ph}}$. We show only some Hartree and Fock diagrams to illustrate the diagrammatic expansion.