Project in Graphene and Silicene

In: Science

Submitted By allthedreams
Words 4865
Pages 20
PHYS3531 Physics Project

Multi-valley monolayer materials

By
Fok Hong Ting
2010280804

Under the supervision of
Dr. Wang Yao

Content
Acknowledgement 4

Introduction 5 Motivation 5 Project outline 5

Chapter I Tight binding model 6
Basics 6
The secular equation 8
Conclusion 9

Chapter II Graphene 11
Formulation 11 π energy band of graphene 15 σ energy bands of graphene 17 Conclusion 18

Chapter III Silicene 19
Tight Binding Hamiltonian of silicene without SOC 20 Constructing orthogonal basis 21 1st order SOC inclusion 24
Conclusion 26

Chapter IV Edge state of Group IV elements 27
Formulation 27
Graphene edge 29
Silicene edge 32
Conclusion 42

References 43

Appendix 44
List of Figures 44

Acknowledgement

I hereby would like to express my appreciation and respect to my supervisor Dr. Wang Yao. Although I am not a talented student, Dr. Yao provided me timely support and insight in the field of physics. It is my fortune to take part in this final year project under his guidance.
Moreover, I would like to thank Dr. GuiBin Liu and Mr. We Yue for their support and comments.

Introduction

Motivation
One of the most intriguing phenomena in physics is the edge effect in 2-D systems. With the emergence of 2-D monolayer materials, the study of edge states in such material is of fundamental interest as well as practical interest. A well known example of such material is graphene, the discovery of which has lead to a Nobel Prize 2 years ago. It remains a mystery whether its counterpart, silicene, exhibit a similar property. This gives us great…...

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