ABSTRACT
Contents 1.1 Carbon Atom and Its Allotropes .................................................................. 4
1.1.1 Diamond ............................................................................................. 5 1.1.2 Graphite............................................................................................... 5 1.1.3 Fullerenes ............................................................................................ 6
1.2 Graphene .......................................................................................................... 6 1.3 Electronic Structure ....................................................................................... 7
1.3.1 Electronic Structure from DFT ....................................................... 9 1.3.2 Electronic Structure from TB ........................................................ 10 1.3.3 TB Model for Monolayer Graphene .............................................. 11 1.3.4 Eective Hamiltonian and Continuum Limit ............................ 16
1.3.4.1 Continuum Limit ............................................................ 17 1.3.5 Helicity and Chirality ..................................................................... 18 1.3.6 Klein Tunnelling .............................................................................. 19 1.3.7 High Mobility, Minimum Conductivity and Universal
Optical Conductivity ...................................................................... 22
1.1 Carbon Atom and Its Allotropes ere is no material as important as carbon to our life. It is in the food we eat, the clothes we wear, the cosmetics we use and the gasoline that fuels our cars. Its name comes from the Latin word carbo for coal and charcoal. Carbon compounds resist extreme conditions due to their strong and stable bonds. Carbon is also an important element that can form long chains and rings of atoms, which form the basis structure of many compounds in living cells, such as deoxyribonucleic acid (DNA).
