The electronic properties of graphene – Project topics materials

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References Background of carbon material Discovered through exploration earlier as charcoal, carbon was famously named by A.L. Lavoisier in 1789 [1] and is commonly found in nature. It occupies the group IV of period III of the periodic table. The atom is made up of 6 protons, 6 electrons, and “A” neutrons which can assume any of 6, 7 and 8 value to form the isotopes 12C, 13C, and 14C, respectively. While the first two isotopes are stable, 12C with a nuclear spin I=0 is the most abundant with 99% occurrence among the carbon isotopes in nature. 13C, with a nuclear spin I=1/2, is the next with 1% of all carbon atoms. 14C rarely occurs; nevertheless, it is vital for archaeological dating to estimate the biological activity of organic materials. In general, carbon has many allotropes such as graphite, diamond, fullerene, carbon nanotubes (CNTs), and graphene. Thermodynamically, all the allotropes formed by carbon are stable and the carbon can react under a high temperature with oxygen to form carbon dioxide [2]. In the ground state, the configuration of the 6 electrons is given as 1s22s22p2. The inner shell (1s) is occupied by two electrons and does not take part in chemical reactions. The remaining 4 electrons occupy 2s and 2p orbitals. Since the energy of the 2p orbitals ( ?? , ?? , and ??) is 4 eV higher than 2s, the 2p orbital is filled with the last two electrons after 2 s.
However, it is energetically more favourable to promote one electron from 2s to 2??, in order to be able to form covalent bonds with other atoms such as H, O, C and etc. The energy gained from such covalent bond is higher than 4 eV that must be overcome in the electronic excitation. In the excited state, four equivalent quantum orbitals 2?, 2?? , 2?? and 2?? are formed. The superposition of the state |2?⟩ with n |2?? ⟩ states is termed spn hybridization. Where n=1, 2 or 3 and j=x, y, or z.

Chapter 1 Introduction
1.1 Background and motivation
1.2 Aims and objectives
1.3 Thesis outline
References
Chapter 2 Literature Review
2.1 Background of carbon material
2.2 Hybridization in carbon
2.2.1 Diamond—sp3 hybridization
2.2.2 Graphene and graphite—sp2 hybridization
2.3 Graphene
2.3.1 The graphene structure
2.3.2 The electronic properties of graphene
2.3.3 The electronic density of state (DOS) of graphene
2.3.4 The vibrational properties of graphene
2.3.5 The optical properties of graphene
2.4 Band-gap modification in graphene
2.5 The review of first-principles studies on graphene
References
Chapter 3 Theoretical background
3.1 The electronic structure calculations
3.1.1 Adiabatic or Born-Oppenheimer approximation [1]
3.1.2 The variational principle
3.1.3 The Hartree approximation
3.1.4 The Hartree-Fock (HF) approximation
3.1.5 Density functional theory
3.1.6 Hohenberg-Kohn theorem
3.1.7 Kohn-Sham scheme
3.1.8 Kohn-Sham variational equations.
3.2 The exchange-correlation energy
3.2.1 Local density approximation (LDA
3.2.2 The generalized gradient approximation (GGA)
3.2.3 The hybrid functionals
3.3 The electron-ion interaction
3.3.1 Pseudopotential method
3.4 Formalism of Kohn-Sham equation in momentum space
3.5 Geometry optimization
3.6 Computational code
References
Chapter 4
4.1 Introduction
4.2 Test of convergence
4.3 Exploring the stability and electronic structure of beryllium and sulphur co-doped graphene: a first principles study
References
4.4 A systematic study of the stability, electronic and optical properties of beryllium and nitrogen co-doped graphene
References
4.5 Ab-initio study of the optical properties of beryllium-sulphur co-doped graphene
Chapter 5 Concluding Remarks and Recommendations
5.1 Conclusions
5.2 Recommendations