Spin-orbit coupling (SOC) is a relativistic effect whose origin lies in the Dirac’s equation – a relativistic analogue of Schrödinger’s equation. SOC corrects the electronic states of a quantum mechanical system up to ~1 eV in case of semiconductors and ~ 2 – 3.6 eV in case of actinides and heavy elements by considering not only the coordinates but also the spin of the electrons in the system. Most of the applications of the present day technology are based on manipulating the electronic structure of a system with very high accuracy and precision. This demands availability of correct electronic structure of a material or molecule within a feasible computational time.
Some direct consequences of SOC in materials can be noticed in analyzing the charge-transport properties of a semiconductor, evaluating the candidature of transition metal dichalcogenides (TMDCs) for spintronic, twistronic and valleytronic applications, and in the origin of topological properties of a material. Not only in materials but also in molecules the SOC effects can be observed. Fine-structure of atomic spectra was explained on the account of SOC. Several additional peaks and wavelength shift in UV-vis spectroscopy of Gold Superatoms can only be explained by correctly considering the energy level splittings caused by SOC. SOC allows intersystem and reverse intersystem crossing by mixing the spin states, ultimately opening various chemical reaction pathways which were spin forbidden before.
Current advancements in computational power enrich us to work shoulder to shoulder with experiments where one can simulate the synthesized structures containing thousands of atoms using semi-empirical methods as in DFTB, GFN-XTB. These methods so far considered SOC effects but only as case studies in testing the implementation of SOC Hamiltonian rather than a systemic extension of SOC parameters to most part of the periodic table and studying SOC effects for different categories of materials and molecules. This motivated us to implement the SOC either in the form of highly accurate parameters throughout the periodic table or as addition in hamiltonian in such methods. Twisted van der Waals 2D materials as in twisted TMDC bilayers shows exciting electronic and optoelectronic properties and depending on the twist angle and chemical composition they can have thousands of atoms in their superlattices. A correct electronic analysis of such structures with SOC corrected DFT is computationally very expensive but is feasible at semi-empirical level. Here, we have applied our implementation on TMDC homo and heterobilayer twisted superlattices and studied the effect of SOC on the excitonic properties of the system. Therefore, this work opens the way for realizing various exotic applications of present day materials as well as molecules.:Table of Contents
Abstract 4
1 Introduction 8
1.1 Quantum Chemistry: 8
1.2 HF based Semi-Empirical Methods 9
1.3 DFT based Semi-Empirical Methods 11
1.3.1 Density Functional based Tight-Binding Method (DFTB) 11
1.3.2 Geometry, Frequency, Non-Covalent, extended Tight Binding (GFN-xTB) 12
1.4 Spin-Orbit Coupling (SOC) 14
1.4.1 SOC in Materials 18
1.4.2 SOC in Molecular Structures 22
1.5 Theoretical Models for Accounting SOC 24
1.6 Motivation, Objective and Outline of thesis 26
2 Methodology 29
2.1 Quantum Chemistry 30
2.1.1 Schrödinger equation 30
2.2 Density Functional Theory 33
2.2.1 Generalized Gradient Approximations 39
2.3 Spin-orbit Coupling (SOC) 41
2.3.1 Classical Picture of SOC in LS model 42
2.3.2 Quantum Picture of SOC in LS model: 43
2.3.3 Calculation of SOC Paramentes 45
2.4 Density Functional Based Semi-empirical Quantum Mechanical Methods 48
2.4.1 Self-Consistent Charge Density Functional Based Tight Binding Method (SCC-DFTB) 48
2.4.2 Extended Tight-Binding (GFN1-xTB) 51
2.4.3 Addition of Spin-Orbit Coupling Hamiltonian in DFTB and GFN-xTB 54
3 Benchmarking Spin-Orbit Coupling Parameters for DFTB 56
3.1 Introduction 58
3.2 Computational Details of the DFT benchmark calculations 60
3.3 Benchmarking Spin-Orbit Coupling Parameters 60
3.3.1 III-V Bulk Semiconductor 61
3.3.2 Transition Metal Dichalcogenide 2D Crystals 65
3.3.3 Topological Insulators 68
3.4 Conclusions 70
4 Spin-Orbit Coupling Corrections for the GFN-xTB method 71
4.1.1 Introduction 73
4.2 Computational Details of The Benchmark Calculations 75
4.3 Results & Discussion 76
4.3.1 Geometries 76
4.3.2 Effect of SOC on Charge Transport Properties of Chromophores in MOFs 77
4.3.3 Superatoms 82
4.3.4 Effect of SOC on Binding of O2 on Ferrous Deoxyheme 85
4.4 Conclusions 86
5 Spin Orbit Coupling Effects on The Excitonic Properties of Twisted Moiré Transition Metal Dichalcogenides 88
5.1 Introduction 90
5.2 Computational Details 92
5.3 Results & Discussions 93
5.4 Excitons in Twisted Moiré Homobilayers 93
5.5 Excitons in Twisted Moiré Heterobilayers 102
5.6 Conclusions 109
6 Summary 112
A. Acronym 116
B. Appendices 120
SOC Parameters 120
7 References 147
C. Acknowledgement 173
| Identifer | oai:union.ndltd.org:DRESDEN/oai:qucosa:de:qucosa:89045 |
| Date | 28 February 2024 |
| Creators | Jha, Gautam |
| Contributors | Heine, Thomas, Hourahine, Benjamin, Technische Universität Dresden, Helmholtz Zentrum Rossendorf |
| Source Sets | Hochschulschriftenserver (HSSS) der SLUB Dresden |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/publishedVersion, doc-type:doctoralThesis, info:eu-repo/semantics/doctoralThesis, doc-type:Text |
| Rights | info:eu-repo/semantics/openAccess |
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